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A294336
Number of ways to write n as a finite power-tower a^(b^(c^...)) of positive integers greater than one.
18
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, 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, 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
OFFSET
1,4
COMMENTS
Möbius-transform of A294337. - Antti Karttunen, Jun 12 2018
LINKS
FORMULA
a(1) = 1; for n > 1, a(n) = Sum_{d|A052409(n)} a(d). - Antti Karttunen, Jun 12 2018, after Mathematica-code.
a(n) = A294337(A052409(n)) for n >= 2. - Pontus von Brömssen, Aug 20 2024
EXAMPLE
The a(4096) = 7 ways are: 2^12, 4^6, 8^4, 8^(2^2), 16^3, 64^2, 4096.
MATHEMATICA
Array[1+Sum[#0[g], {g, Rest[Divisors[GCD@@FactorInteger[#1][[All, 2]]]]}]&, 200]
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))); \\ Antti Karttunen, Jun 12 2018, after Mathematica-code.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 28 2017
EXTENSIONS
More terms from Antti Karttunen, Jun 12 2018
STATUS
approved