This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A294336 #14 Aug 21 2024 06:09:22
%S A294336 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 A294336 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 A294336 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 A294336 Number of ways to write n as a finite power-tower a^(b^(c^...)) of positive integers greater than one.
%C A294336 Möbius-transform of A294337. - _Antti Karttunen_, Jun 12 2018
%H A294336 Antti Karttunen, <a href="/A294336/b294336.txt">Table of n, a(n) for n = 1..65537</a>
%F A294336 a(1) = 1; for n > 1, a(n) = Sum_{d|A052409(n)} a(d). - _Antti Karttunen_, Jun 12 2018, after Mathematica-code.
%F A294336 a(n) = A294337(A052409(n)) for n >= 2. - _Pontus von Brömssen_, Aug 20 2024
%e A294336 The a(4096) = 7 ways are: 2^12, 4^6, 8^4, 8^(2^2), 16^3, 64^2, 4096.
%t A294336 Array[1+Sum[#0[g],{g,Rest[Divisors[GCD@@FactorInteger[#1][[All,2]]]]}]&,200]
%o A294336 (PARI)
%o A294336 A052409(n) = { my(k=ispower(n)); if(k, k, n>1); }; \\ From A052409
%o A294336 A294336(n) = if(1==n,n,sumdiv(A052409(n),d,A294336(d))); \\ _Antti Karttunen_, Jun 12 2018, after Mathematica-code.
%Y A294336 Cf. A000041, A001055, A001597, A007916, A052409, A052410, A089723, A164336, A277562, A284639, A288636, A294337, A294338, A294339, A375598, A375599.
%K A294336 nonn
%O A294336 1,4
%A A294336 _Gus Wiseman_, Oct 28 2017
%E A294336 More terms from _Antti Karttunen_, Jun 12 2018