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 A296116 Number of partitions in which each summand, s, may be used with frequency f if f divides s. 1
 1, 1, 1, 2, 3, 4, 4, 6, 9, 12, 14, 18, 23, 29, 35, 43, 56, 68, 82, 100, 122, 147, 174, 209, 252, 302, 356, 421, 500, 589, 690, 808, 952, 1110, 1292, 1505, 1756, 2034, 2348, 2715, 3139, 3620, 4156, 4778, 5492, 6296, 7195, 8220, 9398, 10714, 12194, 13872, 15784 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 Index entries for related partition-counting sequences FORMULA G.f.: Product_{n >= 1} (1 + Sum_{d divides n} x^(d*n)). EXAMPLE For n=3, the partitions counted are 3 and 2+1. For n=4: 4, 3+1, 2+2. For n=5: 5, 4+1, 3+2, 2+2+1. MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1 or n<0, 0, b(n, i-1)+add(b(n-i*j, i-1), j=numtheory[divisors](i)))) end: a:= n-> b(n\$2): seq(a(n), n=0..60); # Alois P. Heinz, Dec 05 2017 MATHEMATICA iend = 30; s = Series[Product[1 + Sum[x^(Divisors[n][[i]] n), {i, 1, Length[Divisors[n]]}], {n, 1, iend}], {x, 0, iend}]; Print[s]; CoefficientList[s, x] CROSSREFS Cf. A100471, A100881, A100882, A100883. Sequence in context: A326575 A331848 A290728 * A017832 A347713 A056880 Adjacent sequences: A296113 A296114 A296115 * A296117 A296118 A296119 KEYWORD nonn AUTHOR David S. Newman, Dec 04 2017 EXTENSIONS More terms from Alois P. Heinz, Dec 05 2017 STATUS approved

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Last modified August 13 04:16 EDT 2024. Contains 375113 sequences. (Running on oeis4.)