A308367 -id:A308367 - cp's OEIS frontend

A076717 a(n) = -Sum_{d|n} (-n/d)^d.

1, 1, 4, -1, 6, 4, 8, -25, 37, 16, 12, -106, 14, 92, 384, -561, 18, -65, 20, -706, 2552, 1948, 24, -15658, 3151, 8048, 20440, -2570, 30, -33326, 32, -135393, 178512, 130816, 94968, -583219, 38, 523964, 1596560, -2465370, 42, -2521186, 44, -15082, 16364502, 8388124, 48, -78560082, 823593, 23888231

Offset: 1

Vladeta Jovovic, Oct 27 2002

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Seiichi Manyama, Table of n, a(n) for n = 1..5000

Cf. A055225, A308367, A321438.

a(n) = -sumdiv(n, d, (-n/d)^d); \\ Michel Marcus, Mar 22 2021

G.f.: Sum_{n>0} n*x^n/(1+n*x^n).

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

Original entry on oeis.org

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

Seiichi Manyama, Mar 23 2021

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

Cf. A308367, A321438, A342628.

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

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

my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1+(k*x)^k)))

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

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

cp's OEIS Frontend

A076717 a(n) = -Sum_{d|n} (-n/d)^d.

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

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