A342828 a(n) = Sum_{d|n} (-1)^(n/d+1) * d^(n-d).

1, 0, 2, -4, 2, -11, 2, -320, 731, -2869, 2, -1827, 2, -819447, 10297068, -33570816, 2, 1775078476, 2, -36222872973, 678610493340, -285310622035, 2, 169888943418701, 95367431640627, -302875089815037, 150094917726535604, -569376395999240231, 2, 104002456598734754865, 2

Offset

1,3

Links

Seiichi Manyama, Table of n, a(n) for n = 1..599

Formula

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

If p is an odd prime, a(p) = 2.

Mathematica

a[n_] := DivisorSum[n, (-1)^(n/# + 1) * #^(n - #) &]; Array[a, 30] (* Amiram Eldar, Mar 23 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, (-1)^(n/d+1)*d^(n-d));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1+(k*x)^k)))

Crossrefs

Cf. A308367, A321438, A342628.

Sequence in context: A247085 A320971 A360667 * A286958 A332401 A125755

Adjacent sequences: A342825 A342826 A342827 * A342829 A342830 A342831

Keyword

sign

Author

Seiichi Manyama, Mar 23 2021

Status

approved