A359090 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.

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, 2097151, 3276800, 4194302, 2097150, 33554432, 16777214, 66715648, 33554430, 184549374, 134217728, 536870910, 1073741824

Offset: 0

Author

Ilya Gutkovskiy, Dec 16 2022

Keywords

• sign

Links

• Daniel Suteu, Table of n, a(n) for n = 0..41
• Lucas A. Brown, Python program.
• Eric Weisstein's World of Mathematics, Prime Factor
• Eric Weisstein's World of Mathematics, Tetrahedral Number

Crossrefs

Cf. A000292, A001222, A076550, A358927, A359089.

Programs

PARI

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))); \\ Daniel Suteu, Dec 30 2022

Extensions

a(27)-a(34) from Daniel Suteu, Dec 30 2022

a(35)-a(38) from Lucas A. Brown, Sep 11 2024