Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #16 Jan 09 2021 08:37:55
%S 16,19683,314928,298023223876953125,4768371582031250000,
%T 5865991115570068359375,93855857849121093750000,
%U 256923577521058878088611477224235621321607,4110777240336942049417783635587769941145712,5057026776347001897418139706204629734473190581
%N 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).
%H Amiram Eldar, <a href="/A089232/b089232.txt">Table of n, a(n) for n = 1..267</a>
%F Sum_{n>=1} 1/a(n) = - 1 + Product_{p prime} (1 + 1/p^(p^2)) = 0.06255398059238937510... - _Amiram Eldar_, Jan 09 2021
%t 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 *)
%K easy,nonn
%O 1,1
%A _Sam Alexander_, Dec 11 2003
%E More terms from _Harvey P. Dale_, Feb 26 2012