A294336 Number of ways to write n as a finite power-tower a^(b^(c^...)) of positive integers greater than one.

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

Antti Karttunen, Table of n, a(n) for n = 1..65537

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.

Crossrefs

Cf. A000041, A001055, A001597, A007916, A052409, A052410, A089723, A164336, A277562, A284639, A288636, A294337, A294338, A294339, A375598, A375599.

Sequence in context: A089723 A363741 A305253 * A316782 A326647 A326028

Adjacent sequences: A294333 A294334 A294335 * A294337 A294338 A294339

Keyword

nonn

Author

Gus Wiseman, Oct 28 2017

Extensions

More terms from Antti Karttunen, Jun 12 2018

Status

approved