NAME
Sidef::Types::Range::RangeNumber
DESCRIPTION
This class represents numerical ranges in Sidef, providing functionality for iterating over sequences of numbers with a specified start, end, and step value. It supports operations on ranges including arithmetic progressions, number-theoretic functions (like finding primes, semiprimes, squarefree numbers), and various aggregation methods (sum, product, average).
SYNOPSIS
var r = RangeNumber(1, 10) # range from 1 to 10, step 1
var r = RangeNumber(1, 10, 2) # range from 1 to 10, step 2
var r = 1..10 # same as RangeNumber(1, 10)
var r = ^10 # range from 0 to 9INHERITS
Inherits methods from:
* Sidef::Types::Range::Range
* Sidef::Object::ObjectMETHODS
Π
self. Π
self.Π(block)Returns the product of all elements in the range. When a block is provided, returns the product of the block applied to each element.
say (1..5).Π #=> 120 (1*2*3*4*5)
say (1..5).Π {|n| n**2 } #=> 14400 (1*4*9*16*25)Aliases: prod
Σ
self. Σ
self.Σ(block)Returns the sum of all elements in the range. When a block is provided, returns the sum of the block applied to each element.
say (1..10).Σ #=> 55
say (1.. 10).Σ {|n| n**2 } #=> 385Aliases: sum
almost_prime_count
self.almost_prime_count(k)Returns the count of k-almost prime numbers in the range. A k-almost prime is a number with exactly k prime factors (counted with multiplicity).
say (1.. 100).almost_prime_count(2) # count of semiprimes in rangealmost_primes
self. almost_primes(k)Returns an array of k-almost prime numbers in the range. A k-almost prime is a number with exactly k prime factors (counted with multiplicity).
say (1.. 100).almost_primes(2) # semiprimes: [4, 6, 9, 10, 14, ...]
say (1.. 100).almost_primes(3) # 3-almost primes: [8, 12, 18, 20, ...]almost_prime_sum
self.almost_prime_sum(k)Returns the sum of all k-almost prime numbers in the range.
say (1..100).almost_prime_sum(2) # sum of semiprimes in rangeavg
self.avg
self.avg(block)Returns the arithmetic mean of all elements in the range. When a block is provided, returns the average of the block applied to each element.
say (1..10).avg #=> 5.5
say (1..10).avg {|n| n**2 } #=> 38.5avg_by
self.avg_by(block)Returns the arithmetic mean of the block applied to each element in the range.
say (1..10).avg_by {|n| n**2 } #=> 38.5bsearch
self. bsearch(block)Performs a binary search on the range using the given block. Returns the element for which the block returns 0 (equal), or nil if not found.
# Find x where x**2 == 49
say (1..100).bsearch {|n| 49 <=> n**2 } #=> 7bsearch_ge
self.bsearch_ge(block)Performs a binary search and returns the first element for which the block returns >= 0.
say (1..100).bsearch_ge {|n| n**2 - 50 } # first n where n**2 >= 50bsearch_le
self. bsearch_le(block)Performs a binary search and returns the last element for which the block returns <= 0.
say (1..100).bsearch_le {|n| n**2 - 50 } # last n where n**2 <= 50carmichael
self.carmichael(k)Returns the Carmichael numbers in the range that are also k-almost primes. Carmichael numbers are composite numbers n that satisfy a^(n-1) ≡ 1 (mod n) for all integers a coprime to n.
say (1..10000).carmichael(3) # 3-factor Carmichael numberscomposite_count
self. composite_countReturns the count of composite numbers in the range.
say (1..100).composite_count #=> 74composites
self. compositesReturns an array of composite numbers in the range.
say (1..20).composites #=> [4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20]composite_sum
self.composite_sumReturns the sum of all composite numbers in the range.
say (1..100).composite_sumcubefree
self.cubefreeReturns an array of cubefree numbers in the range. A cubefree number has no perfect cube (other than 1) as a divisor.
say (1..20).cubefree #=> [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20]cubefree_count
self.cubefree_countReturns the count of cubefree numbers in the range.
say (1..1000).cubefree_countcubefree_sum
self.cubefree_sumReturns the sum of all cubefree numbers in the range.
say (1..100).cubefree_sumcubefull
self.cubefullReturns an array of cubefull (3-powerful) numbers in the range. A cubefull number has all prime factors appearing at least 3 times.
say (1.. 1000).cubefull #=> [1, 8, 16, 27, 32, 64, 81, ...]cubefull_count
self.cubefull_countReturns the count of cubefull numbers in the range.
say (1..10000).cubefull_countcubefull_sum
self.cubefull_sumReturns the sum of all cubefull numbers in the range.
say (1..1000).cubefull_sumeach_almost_prime
self.each_almost_prime(k, block)Iterates over all k-almost prime numbers in the range, executing the block for each.
(1..100).each_almost_prime(2, {|n| say n }) # print semiprimeseach_carmichael
self.each_carmichael(k, block)Iterates over all Carmichael numbers in the range that are also k-almost primes.
(1.. 100000).each_carmichael(3, {|n| say n })each_composite
self.each_composite(block)Iterates over all composite numbers in the range, executing the block for each.
(1..20).each_composite {|n| say n }each_cubefree
self.each_cubefree(block)Iterates over all cubefree numbers in the range, executing the block for each.
(1..100).each_cubefree {|n| say n }each_cubefull
self.each_cubefull(block)Iterates over all cubefull numbers in the range, executing the block for each.
(1..1000).each_cubefull {|n| say n }each_lucas_carmichael
self.each_lucas_carmichael(k, block)Iterates over all Lucas-Carmichael numbers in the range that are also k-almost primes. Lucas-Carmichael numbers are similar to Carmichael numbers but defined using the relation (p+1) | (n+1) for all prime factors p.
(1.. 100000).each_lucas_carmichael(3, {|n| say n })each_noncubefree
self. each_noncubefree(block)Iterates over all non-cubefree numbers in the range (numbers divisible by a perfect cube > 1).
(1.. 100).each_noncubefree {|n| say n } # 8, 16, 24, 27, ...each_nonpowerfree
self.each_nonpowerfree(k, block)Iterates over all non-k-powerfree numbers in the range (numbers divisible by a k-th power > 1).
(1.. 100).each_nonpowerfree(2, {|n| say n }) # non-squarefree numberseach_nonsquarefree
self.each_nonsquarefree(block)Iterates over all non-squarefree numbers in the range (numbers divisible by a perfect square > 1).
(1..100).each_nonsquarefree {|n| say n } # 4, 8, 9, 12, 16, ...each_omega_prime
self.each_omega_prime(k, block)Iterates over all k-omega prime numbers in the range. A k-omega prime has exactly k distinct prime factors.
(1.. 100).each_omega_prime(2, {|n| say n }) # numbers with exactly 2 distinct prime factorseach_powerfree
self.each_powerfree(k, block)Iterates over all k-powerfree numbers in the range (numbers not divisible by any k-th power > 1).
(1..100).each_powerfree(2, {|n| say n }) # squarefree numberseach_powerful
self.each_powerful(k, block)Iterates over all k-powerful numbers in the range. A k-powerful number has all prime factors appearing at least k times.
(1..1000).each_powerful(2, {|n| say n }) # squarefull numberseach_prime
self.each_prime(block)Iterates over all prime numbers in the range, executing the block for each.
(1..100).each_prime {|p| say p } # print primes up to 100each_prime_power
self.each_prime_power(block)Iterates over all prime powers in the range. A prime power is p^k where p is prime and k >= 1.
(1..100).each_prime_power {|n| say n } # 2, 3, 4, 5, 7, 8, 9, 11, ...each_semiprime
self.each_semiprime(block)Iterates over all semiprimes (2-almost primes) in the range. A semiprime is a product of exactly two primes.
(1..100).each_semiprime {|n| say n } # 4, 6, 9, 10, 14, 15, ...each_squarefree
self.each_squarefree(block)Iterates over all squarefree numbers in the range, executing the block for each.
(1..100).each_squarefree {|n| say n }each_squarefree_almost_prime
self.each_squarefree_almost_prime(k, block)Iterates over all squarefree k-almost prime numbers in the range.
(1.. 100).each_squarefree_almost_prime(3, {|n| say n }) # products of 3 distinct primeseach_squarefree_semiprime
self.each_squarefree_semiprime(block)Iterates over all squarefree semiprimes in the range (products of two distinct primes).
(1..100).each_squarefree_semiprime {|n| say n } # 6, 10, 14, 15, ...each_squarefull
self.each_squarefull(block)Iterates over all squarefull (2-powerful) numbers in the range. A squarefull number has all prime factors appearing at least twice.
(1..100).each_squarefull {|n| say n } # 1, 4, 8, 9, 16, 25, 27, ...faulhaber
self.faulhaber(k)Returns the sum of the k-th powers of all integers in the range using Faulhaber's summation formula.
say (1..10).faulhaber(2) #=> 385 (sum of squares: 1+4+9+... +100)
say (1.. 10).faulhaber(3) #=> 3025 (sum of cubes: 1+8+27+... +1000)Aliases: faulhaber_sum
gcd
self. gcd
self.gcd(block)Returns the greatest common divisor of all elements in the range. When a block is provided, returns the GCD of the block applied to each element.
say (6..12).gcd # GCD of 6,7,8,9,10,11,12
say (1..10).gcd {|n| n * 6 } # GCD of 6,12,18,... ,60gcd_by
self.gcd_by(block)Returns the greatest common divisor of the block applied to each element in the range.
say (1..10).gcd_by {|n| 2*n }iter
self.iterReturns an iterator (Block) that generates successive elements of the range.
var it = (1..5).iter
say it.run #=> 1
say it.run #=> 2
say it.run #=> 3lcm
self. lcm
self.lcm(block)Returns the least common multiple of all elements in the range. For the range 1..n with step 1, this uses an optimized consecutive LCM formula.
say (1..10).lcm #=> 2520
say (1.. 10).lcm {|n| 2*n }lcm_by
self. lcm_by(block)Returns the least common multiple of the block applied to each element in the range.
say (1.. 10).lcm_by {|n| n + 1 }lucas_carmichael
self.lucas_carmichael(k)Returns the Lucas-Carmichael numbers in the range that are also k-almost primes.
say (1..100000).lucas_carmichael(3)mertens
self.mertensReturns the Mertens function M(n) = Σμ(k) for k in the range, where μ is the Möbius function.
say (1..100).mertensnew
RangeNumber. new(from, to, step)Creates a new RangeNumber object with the specified start, end, and optional step value.
var r = RangeNumber.new(1, 10) # 1 to 10, step 1
var r = RangeNumber.new(1, 10, 2) # 1, 3, 5, 7, 9
var r = RangeNumber.new(10) # 0 to 9Aliases: call
noncubefree
self.noncubefreeReturns an array of non-cubefree numbers in the range (numbers divisible by a perfect cube > 1).
say (1..100).noncubefree #=> [8, 16, 24, 27, 32, ...]noncubefree_count
self. noncubefree_countReturns the count of non-cubefree numbers in the range.
say (1..1000).noncubefree_countnoncubefree_sum
self. noncubefree_sumReturns the sum of all non-cubefree numbers in the range.
say (1..100).noncubefree_sumnonpowerfree
self. nonpowerfree(k)Returns an array of non-k-powerfree numbers in the range.
say (1..100).nonpowerfree(2) # non-squarefree numbersnonpowerfree_count
self.nonpowerfree_count(k)Returns the count of non-k-powerfree numbers in the range.
say (1.. 1000).nonpowerfree_count(2)nonpowerfree_sum
self.nonpowerfree_sum(k)Returns the sum of all non-k-powerfree numbers in the range.
say (1.. 100).nonpowerfree_sum(2)nonsquarefree
self.nonsquarefreeReturns an array of non-squarefree numbers in the range (numbers divisible by a perfect square > 1).
say (1..50).nonsquarefree #=> [4, 8, 9, 12, 16, 18, 20, 24, 25, ...]nonsquarefree_count
self. nonsquarefree_countReturns the count of non-squarefree numbers in the range.
say (1..1000).nonsquarefree_countnonsquarefree_sum
self.nonsquarefree_sumReturns the sum of all non-squarefree numbers in the range.
say (1..100).nonsquarefree_sumomega_prime_count
self. omega_prime_count(k)Returns the count of k-omega prime numbers in the range (numbers with exactly k distinct prime factors).
say (1..1000).omega_prime_count(2) # numbers with exactly 2 distinct prime factorsomega_primes
self. omega_primes(k)Returns an array of k-omega prime numbers in the range.
say (1..100).omega_primes(2) # numbers with exactly 2 distinct prime factorsomega_prime_sum
self.omega_prime_sum(k)Returns the sum of all k-omega prime numbers in the range.
say (1.. 1000).omega_prime_sum(2)powerfree
self.powerfree(k)Returns an array of k-powerfree numbers in the range (numbers not divisible by any k-th power > 1).
say (1..50).powerfree(2) # squarefree numbers
say (1.. 50).powerfree(3) # cubefree numberspowerfree_count
self. powerfree_count(k)Returns the count of k-powerfree numbers in the range.
say (1..1000).powerfree_count(2) # count of squarefree numberspowerfree_sum
self.powerfree_sum(k)Returns the sum of all k-powerfree numbers in the range.
say (1..100).powerfree_sum(2)powerful
self.powerful(k)Returns an array of k-powerful numbers in the range. A k-powerful number has all prime factors appearing at least k times.
say (1..100).powerful(2) # squarefull: [1, 4, 8, 9, 16, 25, 27, ...]powerful_count
self.powerful_count(k)Returns the count of k-powerful numbers in the range.
say (1..10000).powerful_count(2)powerful_sum
self.powerful_sum(k)Returns the sum of all k-powerful numbers in the range.
say (1..1000).powerful_sum(2)prime_count
self. prime_countReturns the count of prime numbers in the range.
say (1..100).prime_count #=> 25prime_power_count
self.prime_power_countReturns the count of prime powers in the range (numbers of the form p^k where p is prime and k >= 1).
say (1..100).prime_power_countprime_powers
self.prime_powersReturns an array of prime powers in the range.
say (1..50).prime_powers #=> [2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49]prime_power_sum
self.prime_power_sumReturns the sum of all prime powers in the range.
say (1..100).prime_power_sumprimes
self.primesReturns an array of prime numbers in the range.
say (1..50).primes #=> [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]prime_sum
self.prime_sumReturns the sum of all prime numbers in the range.
say (1..100).prime_sum #=> 1060prod_by
self. prod_by(block)Returns the product of the block applied to each element in the range.
say (1.. 5).prod_by {|n| n + 1 } #=> 720 (2*3*4*5*6)rough_count
self.rough_count(k)Returns the count of k-rough numbers in the range. A k-rough number has all prime factors >= k.
say (1..1000).rough_count(5) # numbers with all prime factors >= 5semiprime_count
self.semiprime_countReturns the count of semiprimes (products of exactly two primes) in the range.
say (1..100).semiprime_countsemiprimes
self.semiprimesReturns an array of semiprimes in the range.
say (1..50).semiprimes #=> [4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49]semiprime_sum
self.semiprime_sumReturns the sum of all semiprimes in the range.
say (1..100).semiprime_sumsmooth_count
self.smooth_count(k)Returns the count of k-smooth numbers in the range. A k-smooth number has all prime factors <= k.
say (1..1000).smooth_count(5) # 5-smooth numbers (regular numbers)squarefree
self.squarefreeReturns an array of squarefree numbers in the range. A squarefree number has no perfect square (other than 1) as a divisor.
say (1..20).squarefree #=> [1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19]squarefree_almost_prime_count
self.squarefree_almost_prime_count(k)Returns the count of squarefree k-almost prime numbers in the range (products of exactly k distinct primes).
say (1.. 1000).squarefree_almost_prime_count(3)squarefree_almost_primes
self. squarefree_almost_primes(k)Returns an array of squarefree k-almost prime numbers in the range.
say (1..100).squarefree_almost_primes(3) # products of 3 distinct primes: [30, 42, 66, 70, 78]squarefree_almost_prime_sum
self.squarefree_almost_prime_sum(k)Returns the sum of all squarefree k-almost prime numbers in the range.
say (1.. 1000).squarefree_almost_prime_sum(3)squarefree_count
self.squarefree_countReturns the count of squarefree numbers in the range.
say (1.. 100).squarefree_count #=> 61squarefree_semiprime_count
self.squarefree_semiprime_countReturns the count of squarefree semiprimes in the range (products of two distinct primes).
say (1.. 100).squarefree_semiprime_countsquarefree_semiprimes
self.squarefree_semiprimesReturns an array of squarefree semiprimes in the range.
say (1..50).squarefree_semiprimes #=> [6, 10, 14, 15, 21, 22, 26, 33, 34, 35, 38, 39, 46]squarefree_semiprime_sum
self.squarefree_semiprime_sumReturns the sum of all squarefree semiprimes in the range.
say (1..100).squarefree_semiprime_sumsquarefree_sum
self.squarefree_sumReturns the sum of all squarefree numbers in the range.
say (1..100).squarefree_sumsquarefull
self.squarefullReturns an array of squarefull (2-powerful) numbers in the range. A squarefull number has all prime factors appearing at least twice.
say (1..100).squarefull #=> [1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100]squarefull_count
self.squarefull_countReturns the count of squarefull numbers in the range.
say (1..10000).squarefull_countsquarefull_sum
self.squarefull_sumReturns the sum of all squarefull numbers in the range.
say (1..1000).squarefull_sumsum_by
self. sum_by(block)Returns the sum of the block applied to each element in the range.
say (1..10).sum_by {|n| n**2 } #=> 385to_s
self.to_sReturns a string representation of the range.
say (1..10).to_s #=> "RangeNum(1, 10, 1)"Aliases: dump, to_str