A345274 - OEIS

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

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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