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%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
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