sidef-scripts/Math/primorial_deflation.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# Date: 15 April 2019
# https://github.com/trizen

# Represent a given number as a product of primorials (if possible).

# The sequence of numbers that can be represented as a product of primorials, is given by:
#   https://oeis.org/A025487

# Among other terms, the sequence includes the factorials and the highly composite numbers.

# See also:
#   https://oeis.org/A181815 -- "primorial deflation" of A025487(n)
#   https://oeis.org/A108951 -- "primorial inflation" of n

func primorial_deflation (n) {

    var prod = 1

    while (n > 1) {

        var g = n.gpf          # greatest prime factor
        var p = g.primorial

        n /= p
        n.is_int || return nil

        prod *= g
    }

    return prod
}

func primorial_deflation_bag(n) {

    var prod = 1
    var f = Bag(n.factor...)

    while (f) {
        var p = f.max
        f -= p.primes
        prod *= p
    }

    return prod
}

func primorial_deflation_fast (n) {
    n.factor_prod {|p,e|
        (p / (p > 2 ? p.prev_prime : 1))**e
    }
}

var arr = 15.of { primorial_deflation(_!) }     # https://oeis.org/A307035

say arr                                                     #=> [1, 1, 2, 3, 12, 20, 60, 84, 672, 1512, 5040, 7920, 47520, 56160, 157248]
say arr.map {|n| n.factor_prod {|p,e| p.primorial**e } }    #=> [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200]

assert_eq(15.of { primorial_deflation(_!) }, 15.of { primorial_deflation_bag(_!) })
assert_eq(15.of { primorial_deflation(_!) }, 15.of { primorial_deflation_fast(_!) })

var n = 14742217487368791965347653720647452690286549052234444179664342042930370966727413549068727214664401976854238590421417268673037399536054005777393104248210539172848500736334237168727231561710827753972114334247396552090671649834020135652920430241738510495400044737265204738821393451152066370913670083496651044937158497896720493198891148968218874744806522767468280764179516341996273430700779982929787918221844760577694188288275419541410142336911631623319041967633591283303769044016192030492715535641753600000

say primorial_deflation(n)        #=> 52900585920
say primorial_deflation_bag(n)    #=> 52900585920
say primorial_deflation_fast(n)   #=> 52900585920