A366814 a(n) = Sum_{d|n} (-1)^(n/d-1) * binomial(d+3,4).

1, 4, 16, 29, 71, 115, 211, 289, 511, 649, 1002, 1253, 1821, 2174, 3146, 3505, 4846, 5605, 7316, 8099, 10852, 11653, 14951, 16333, 20546, 21935, 27916, 28904, 35961, 38620, 46377, 48113, 59922, 61204, 74096, 77024, 91391, 93959, 113766, 114059, 135752, 140654, 163186

Offset: 1

Author

Seiichi Manyama, Oct 24 2023

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Partial sums give A366723.

Cf. A000593, A365007, A366813.

Programs

Mathematica

Table[DivisorSum[n, (-1)^(n/# - 1)*Binomial[# + 3, 4] &], {n, 56}] (* Michael De Vlieger, Oct 25 2023 *)

PARI

a(n) = sumdiv(n, d, (-1)^(n/d-1)*binomial(d+3, 4));

Formula

G.f.: -Sum_{k>=1} (-x)^k/(1-x^k)^5 = Sum_{k>=1} binomial(k+3,4) * x^k/(1+x^k).