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A294337 Number of ways to write 2^n as a finite power-tower a^(b^(c^...)) of positive integers greater than one. 8
1, 2, 2, 4, 2, 4, 2, 6, 4, 4, 2, 7, 2, 4, 4, 10, 2, 7, 2, 7, 4, 4, 2, 10, 4, 4, 6, 7, 2, 8, 2, 12, 4, 4, 4, 12, 2, 4, 4, 10, 2, 8, 2, 7, 7, 4, 2, 15, 4, 7, 4, 7, 2, 10, 4, 10, 4, 4, 2, 13, 2, 4, 7, 16, 4, 8, 2, 7, 4, 8, 2, 16, 2, 4, 7, 7, 4, 8, 2, 15, 10, 4, 2, 13, 4, 4, 4, 10, 2, 13, 4, 7, 4, 4, 4, 18, 2, 7, 7, 12, 2, 8, 2, 10, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{d|n} A294336(d) = A294336(A000079(n)). - Antti Karttunen, Jun 12 2018
EXAMPLE
The a(12) = 7 ways are: 2^12, 4^6, 8^4, 8^(2^2), 16^3, 64^2, 4096.
MATHEMATICA
a[n_]:=1+Sum[a[g], {g, Rest[Divisors[GCD@@FactorInteger[n][[All, 2]]]]}];
Table[a[2^n], {n, 100}]
PROG
(PARI)
A052409(n) = { my(k=ispower(n)); if(k, k, n>1); }; \\ From A052409
A294336(n) = if(1==n, n, sumdiv(A052409(n), d, A294336(d)));
A294337(n) = sumdiv(n, d, A294336(d));
\\ Or alternatively, after Mathematica-code as:
A294337(n) = A294336(2^n); \\ Antti Karttunen, Jun 12 2018
CROSSREFS
Sequence in context: A129089 A255201 A169594 * A322327 A124315 A101113
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 28 2017
EXTENSIONS
More terms from Antti Karttunen, Jun 12 2018
STATUS
approved

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Last modified March 29 08:01 EDT 2024. Contains 371265 sequences. (Running on oeis4.)