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A295924
Number of twice-factorizations of n of type (R,P,R).
11
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).
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 30 2017
EXTENSIONS
More terms from Antti Karttunen, Jul 29 2018
STATUS
approved