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%I #23 Dec 30 2020 21:19:39
%S 1,2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,31,32,37,41,43,47,49,53,
%T 59,61,67,71,73,79,81,83,89,97,101,103,107,109,113,121,125,127,128,
%U 131,137,139,149,151,157,163,167,169,173,179,181,191,193,197,199,211,223,227
%N a(1)=1. Thereafter, all terms are primes raised to the values of earlier terms of the sequence.
%C These are the values of exponent towers consisting completely of primes coefficients. (For example, p^(q^(r^(s^..))), all variables being primes.) This sequence first differs from the terms of A096165, after the initial 1 in this sequence, when 18446744073709551616 = 2^64 occurs in A096165 but not in this sequence.
%C A064372(a(n)) = 1. [_Reinhard Zumkeller_, Aug 27 2011]
%H Michael De Vlieger, <a href="/A164336/b164336.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerTower.html">Power Tower</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration">Tetration</a>
%p q:= n-> is(n=1 or (l-> nops(l)=1 and q(l[1, 2]))(ifactors(n)[2])):
%p select(q, [$1..350])[]; # _Alois P. Heinz_, Dec 30 2020
%t Block[{a = {1}}, Do[If[Length@ # == 1 && MemberQ[a, First@ #], AppendTo[a, i]] &[FactorInteger[i][[All, -1]]], {i, 2, 227}]; a] (* _Michael De Vlieger_, Aug 31 2017 *)
%o (PARI) L=1000;S=[1];SS=[];while(#S!=#SS, SS=S;S=[];for(i=1,#SS,forprime(p=2,floor(L^(1/SS[i])),S=concat(S,p^SS[i])));S=eval(setunion(S,SS)));vecsort(S) \\ _Hagen von Eitzen_, Oct 03 2009
%Y Cf. A096165, A164337.
%K nonn
%O 1,2
%A _Leroy Quet_, Aug 13 2009
%E More terms from _Hagen von Eitzen_, Oct 03 2009
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