A340625 a(n) = Sum_{d|n, d odd, d <= n/d} binomial(n/d, d).

1, 2, 3, 4, 5, 6, 7, 8, 10, 10, 11, 16, 13, 14, 25, 16, 17, 38, 19, 20, 56, 22, 23, 80, 26, 26, 111, 28, 29, 156, 31, 32, 198, 34, 56, 256, 37, 38, 325, 96, 41, 406, 43, 44, 626, 46, 47, 608, 50, 302, 731, 52, 53, 870, 517, 64, 1026, 58, 59, 1992, 61, 62, 1429, 64, 1352, 1606, 67, 68, 1840, 2192, 71, 2096, 73, 74

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

G.f.: (1/2) * Sum_{k >= 1} ((1 + x^k)^k - (1 - x^k)^k).

If p is prime, a(p) = p.

Mathematica

a[n_] := DivisorSum[n, Binomial[n/#, #] &, OddQ[#] &]; Array[a, 75] (* Amiram Eldar, Apr 25 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, (d%2)*binomial(n/d, d));
(PARI) N=99; x='x+O('x^N); Vec(sum(k=1, N, (1+x^k)^k-(1-x^k)^k)/2)

Crossrefs

Cf. A318636, A327124, A340626.

Sequence in context: A073295 A191656 A266190 * A347644 A265572 A265556

Adjacent sequences: A340622 A340623 A340624 * A340626 A340627 A340628

Keyword

nonn

Author

Seiichi Manyama, Apr 25 2021

Status

approved