A295924 Number of twice-factorizations of n of type (R,P,R).

1, 1, 1, 3, 1, 1, 1, 4, 3, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 4, 1, 1, 1, 1, 8, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1

Offset

1,4

Comments

a(n) is the number of ways to choose an integer partition of a divisor of A052409(n).

Links

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

Index entries for sequences computed from exponents in factorization of n

Formula

a(1) = 1; for n > 1, a(n) = Sum_{d|A052409(n)} A000041(d). - Antti Karttunen, Jul 29 2018

Example

The a(16) = 8 twice-factorizations are (2)*(2)*(2)*(2), (2)*(2)*(2*2), (2)*(2*2*2), (2*2)*(2*2), (2*2*2*2), (4)*(4), (4*4), (16).

Mathematica

Table[DivisorSum[GCD@@FactorInteger[n][[All, 2]], PartitionsP], {n, 100}]

Prog

(PARI)
A052409(n) = { my(k=ispower(n)); if(k, k, n>1); }; \\ From A052409
A295924(n) = if(1==n, n, sumdiv(A052409(n), d, numbpart(d))); \\ Antti Karttunen, Jul 29 2018

Crossrefs

Cf. A000005, A000041, A001055, A047968, A052409, A052410, A089723, A281113, A284639, A295923, A295931, A295935, A296134.

Sequence in context: A098950 A318873 A346403 * A357669 A361012 A363903

Adjacent sequences: A295921 A295922 A295923 * A295925 A295926 A295927

Keyword

nonn

Author

Gus Wiseman, Nov 30 2017

Extensions

More terms from Antti Karttunen, Jul 29 2018

Status

approved