experimental-projects/oeis-research/Ilya Gutkovskiy/Index of the smallest tetrahedral number with exactly n prime factors (counted with multiplicity), or -1 if no such number exists/prog.sf

#!/usr/bin/ruby

# a(n) is the index of the smallest tetrahedral number with exactly n prime factors (counted with multiplicity), or -1 if no such number exists.
# https://oeis.org/A359090

# Previously known terms:
#   1, -1, 2, 4, 6, 8, 14, 30, 48, 62, 126, 160, 350, 510, 1022, 2046, 1024, 4095, 4094, 13310, 28672, 32768, 65534, 180224, 262142, 360448, 262143

# New terms a(27)-a(34):
#   2097151, 3276800, 4194302, 2097150, 33554432, 16777214, 66715648, 33554430

#`(

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

)

func a(n) {
    for k in (1..Inf) {
        if (pyramidal(k, 3).is_almost_prime(n)) {
            return k
        }
    }
}

for n in (2..100) {
    say "a(#{n}) = #{a(n)}"
}

__END__
a(2) = 2
a(3) = 4
a(4) = 6
a(5) = 8
a(6) = 14
a(7) = 30
a(8) = 48
a(9) = 62
a(10) = 126
a(11) = 160
a(12) = 350
a(13) = 510
a(14) = 1022
a(15) = 2046
a(16) = 1024
a(17) = 4095
a(18) = 4094
a(19) = 13310
a(20) = 28672
a(21) = 32768
a(22) = 65534
a(23) = 180224
a(24) = 262142
a(25) = 360448
a(26) = 262143
a(27) = 2097151
a(28) = 3276800
a(29) = 4194302
a(30) = 2097150
a(31) = 33554432
a(32) = 16777214
a(33) = 66715648
a(34) = 33554430