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A296134 Number of twice-factorizations of n of type (R,Q,R). 5
1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 4, 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, 8, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) is the number of ways to choose a strict 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

From Antti Karttunen, Jul 31 2018: (Start)

a(1) = 1; for n > 1, a(n) = Sum_{d|A052409(n)} A000009(d).

a(n) = A047966(A052409(n)). (End)

EXAMPLE

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

MATHEMATICA

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

PROG

(PARI)

A000009(n, k=(n-!(n%2))) = if(!n, 1, my(s=0); while(k >= 1, if(k<=n, s += A000009(n-k, k)); k -= 2); (s));

A052409(n) = { my(k=ispower(n)); if(k, k, n>1); }; \\ From A052409

A296134(n) = if(1==n, n, sumdiv(A052409(n), d, A000009(d))); \\ Antti Karttunen, Jul 29 2018

CROSSREFS

Cf. A000005, A000009, A001055, A047966, A047968, A052409, A052410, A089723, A281113, A295923, A295924, A295931, A295935, A296133.

Sequence in context: A267115 A328919 A277647 * A306694 A327503 A158052

Adjacent sequences:  A296131 A296132 A296133 * A296135 A296136 A296137

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 05 2017

EXTENSIONS

More terms from Antti Karttunen, Jul 29 2018

STATUS

approved

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Last modified September 21 15:50 EDT 2020. Contains 337272 sequences. (Running on oeis4.)