A321386 a(n) = Sum_{d|n} (-1)^(n/d+1)*d^(d-1).

1, 1, 10, 61, 626, 7768, 117650, 2097085, 43046731, 999999376, 25937424602, 743008362964, 23298085122482, 793714773136496, 29192926025391260, 1152921504604749757, 48661191875666868482, 2185911559738653493015, 104127350297911241532842, 5242879999999998999999436, 278218429446951548637314060

Offset: 1

Author

Ilya Gutkovskiy, Nov 08 2018

Keywords

• nonn

Crossrefs

Cf. A000169, A262843, A321388.

Programs

Mathematica

Table[Sum[(-1)^(n/d + 1) d^(d - 1), {d, Divisors[n]}], {n, 21}]
nmax = 21; Rest[CoefficientList[Series[Sum[k^(k - 1) x^k/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]]

PARI

a(n) = sumdiv(n, d, (-1)^(n/d+1)*d^(d-1)); \\ Michel Marcus, Nov 09 2018

Formula

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

a(n) ~ n^(n-1). - Vaclav Kotesovec, Nov 09 2018