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%I #10 Jun 12 2018 21:15:26
%S 1,1,1,2,1,1,1,2,2,1,1,1,1,1,1,4,1,1,1,1,1,1,1,1,2,1,2,1,1,1,1,2,1,1,
%T 1,2,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,1,1,1,1,
%U 1,1,1,1,1,1,1,1,1,1,1,1,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1
%N Number of ways to write n as a finite power-tower a^(b^(c^...)) of positive integers greater than one.
%C Möbius-transform of A294337. - _Antti Karttunen_, Jun 12 2018
%H Antti Karttunen, <a href="/A294336/b294336.txt">Table of n, a(n) for n = 1..65537</a>
%F a(1) = 1; for n > 1, a(n) = Sum_{d|A052409(n)} a(d). - _Antti Karttunen_, Jun 12 2018, after Mathematica-code.
%e The a(4096) = 7 ways are: 2^12, 4^6, 8^4, 8^(2^2), 16^3, 64^2, 4096.
%t Array[1+Sum[#0[g],{g,Rest[Divisors[GCD@@FactorInteger[#1][[All,2]]]]}]&,200]
%o (PARI)
%o A052409(n) = { my(k=ispower(n)); if(k, k, n>1); }; \\ From A052409
%o A294336(n) = if(1==n,n,sumdiv(A052409(n),d,A294336(d))); \\ _Antti Karttunen_, Jun 12 2018, after Mathematica-code.
%Y Cf. A000041, A001055, A001597, A007916, A052409, A052410, A089723, A164336, A277562, A284639, A288636, A294337, A294338, A294339.
%K nonn
%O 1,4
%A _Gus Wiseman_, Oct 28 2017
%E More terms from _Antti Karttunen_, Jun 12 2018
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