A345275 a(n) = Sum_{d|n} (n-d)^sigma(n/d).

0, 1, 16, 2195, 4096, 244140908, 1679616, 4747561789943, 549755815184, 150094635297261390, 1000000000000, 144209936106499235037680851362, 1283918464548864, 542800770374370513201577400, 3214199700417740936754083600, 2876265888493261300182938548474503919

Offset

1,3

Comments

If p is prime, a(p) = Sum_{d|p} (p-d)^sigma(p/d) = (p-1)^(p+1).

Links

Table of n, a(n) for n=1..16.

Example

a(10) = Sum_{d|10} (10-d)^sigma(10/d) = 9^18 + 8^6 + 5^3 + 0^1 = 150094635297261390.

Mathematica

Table[Sum[(n - k)^DivisorSigma[1, n/k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 20}]

Crossrefs

Cf. A000203 (sigma).

Sequence in context: A101800 A208148 A265593 * A304399 A186857 A196884

Adjacent sequences: A345272 A345273 A345274 * A345276 A345277 A345278

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 12 2021

Status

approved