experimental-projects/oeis-research/Ilya Gutkovskiy/Index of the smallest square pyramidal number with exactly n prime factors (counted with multiplicity)/prog.sf

#!/usr/bin/ruby

# a(n) is the index of the smallest square pyramidal number with exactly n prime factors (counted with multiplicity).
# https://oeis.org/A359193

# Previously known terms:
#   1, 2, 3, 4, 7, 15, 24, 31, 63, 80, 175, 255, 511, 1023, 512, 6912, 2047, 6655, 14336, 16384, 32767, 90112, 131071, 180224, 483327, 1114112

# New terms a(26)-a(34):
#   1638400, 2097151, 1048575, 16777216, 8388607, 33357824, 16777215, 92274687, 67108864

#`(

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

)

func a(n) {
    for k in (1..Inf) {
        if (pyramidal(k, 4).is_almost_prime(n)) {
            return k
        }
    }
}

for n in (1..100) {
    say "a(#{n}) = #{a(n)}"
}

__END__
a(1) = 2
a(2) = 3
a(3) = 4
a(4) = 7
a(5) = 15
a(6) = 24
a(7) = 31
a(8) = 63
a(9) = 80
a(10) = 175
a(11) = 255
a(12) = 511
a(13) = 1023
a(14) = 512
a(15) = 6912
a(16) = 2047
a(17) = 6655
a(18) = 14336
a(19) = 16384
a(20) = 32767
a(21) = 90112
a(22) = 131071
a(23) = 180224
a(24) = 483327
a(25) = 1114112
a(26) = 1638400
a(27) = 2097151
a(28) = 1048575
a(29) = 16777216
a(30) = 8388607
a(31) = 33357824
a(32) = 16777215
a(33) = 92274687
a(34) = 67108864