A089232 Numbers of the form (p1^(p1^2))*(p2^(p2^2))*...*(pk^(pk^2)) where p1,p2,..,pk are distinct primes. (In other words: in the prime factorization of any term, the exponent of p is either 0 or p^2 for all prime p).

16, 19683, 314928, 298023223876953125, 4768371582031250000, 5865991115570068359375, 93855857849121093750000, 256923577521058878088611477224235621321607, 4110777240336942049417783635587769941145712, 5057026776347001897418139706204629734473190581

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..267

Formula

Sum_{n>=1} 1/a(n) = - 1 + Product_{p prime} (1 + 1/p^(p^2)) = 0.06255398059238937510... - Amiram Eldar, Jan 09 2021

Mathematica

seq[max_] := Module[{p = 2, ps = {}, s = {1}, k, n}, While[p^(p^2) < max, AppendTo[ps, p]; p = NextPrime[p]]; n = Length[ps]; Do[p = ps[[k]]; s = Select[Union @ Flatten@Outer[Times, s, {1, p^(p^2)}], # <= max &], {k, 1, n}]; Rest@s]; seq[10^50] (* Amiram Eldar, Jan 09 2021 *)

Crossrefs

Sequence in context: A283720 A349891 A098175 * A300615 A002489 A060205

Adjacent sequences: A089229 A089230 A089231 * A089233 A089234 A089235

Keyword

easy,nonn

Author

Sam Alexander, Dec 11 2003

Extensions

More terms from Harvey P. Dale, Feb 26 2012

Status

approved