OFFSET
1,2
COMMENTS
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.
A064372(a(n)) = 1. [Reinhard Zumkeller, Aug 27 2011]
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Power Tower
Wikipedia, Tetration
MAPLE
q:= n-> is(n=1 or (l-> nops(l)=1 and q(l[1, 2]))(ifactors(n)[2])):
select(q, [$1..350])[]; # Alois P. Heinz, Dec 30 2020
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Aug 13 2009
EXTENSIONS
More terms from Hagen von Eitzen, Oct 03 2009
STATUS
approved