experimental-projects/oeis-research/Ilya Gutkovskiy/Smallest n-gonal pyramidal number with exactly n prime factors (counted with multiplicity)/prog.sf

#!/usr/bin/ruby

# a(n) is the smallest n-gonal pyramidal number with exactly n prime factors (counted with multiplicity).
# https://oeis.org/A358865

# Known terms:
#   20, 140, 405, 2856, 25296, 111720, 25984, 5474000, 237600, 223826688, 3852800, 268565760, 1834725376, 175861400000, 335674368, 2863363937280, 4383831556096, 206015846400, 3400704000, 938209120583680, 2981338216980480, 21463949229465600, 45410367307776, 72056803765911552

#`(

# PARI/GP program:
a(n) = if(n<3, return()); for(k=1, oo, my(t=(k*(k+1)*((n-2)*k + (5-n)))\6); if(bigomega(t) == n, return(t))); \\ ~~~~

# PARI/GP program for A359016
a(n) = if(n<3, return()); for(k=1, oo, my(t=(k*(k+1)*((n-2)*k + (5-n)))\6); if(bigomega(t) == n, return(k))); \\ ~~~~

)

func a(n) {
    for k in (1..Inf) {
        if (pyramidal(k, n).is_almost_prime(n)) {
            return pyramidal(k, n)
        }
    }
}

for n in (30..100) {
    say "a(#{n}) = #{a(n)}"
}

__END__
a(22) = 938209120583680
a(23) = 2981338216980480
a(24) = 21463949229465600
a(25) = 45410367307776
a(26) = 72056803765911552
a(27) = 4803826408397209600
a(28) = 1536502117117468999680
a(29) = 10823784744326529024

__END__

n = 27; k = 1048575
n = 28; k = 7077888
n = 29; k = 1339848