A345274 a(n) = Sum_{d|n} (n-d)^tau(n/d).

0, 1, 4, 31, 16, 650, 36, 2633, 548, 6650, 100, 1782390, 144, 28754, 38660, 799583, 256, 24192515, 324, 47154588, 160520, 195002, 484, 78424725898, 14224, 391370, 471124, 387887498, 784, 500247950884, 900, 912432417, 1049960, 1187234, 1338020, 78818475807611, 1296, 1875818

Offset

1,3

Comments

If p is prime, a(p) = Sum_{d|p} (p-d)^tau(p/d) = (p-1)^2 + 0^1 = (p-1)^2.

Links

Table of n, a(n) for n=1..38.

Example

a(10) = Sum_{d|10} (10-d)^tau(10/d) = 9^4 + 8^2 + 5^2 + 0^1 = 6650.

Mathematica

Table[Sum[(n - k)^DivisorSigma[0, n/k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 50}]

Crossrefs

Cf. A000005 (tau), A174937.

Sequence in context: A103307 A196248 A196246 * A025416 A043082 A371034

Adjacent sequences: A345271 A345272 A345273 * A345275 A345276 A345277

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 12 2021

Status

approved