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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 (list; graph; refs; listen; history; text; internal format)
 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 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 * A123940 A339969 A204120 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

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Last modified August 2 09:22 EDT 2021. Contains 346422 sequences. (Running on oeis4.)