A345273 a(n) = Sum_{d|n} (n-d)^tau(d).

0, 1, 2, 7, 4, 30, 6, 107, 44, 98, 10, 2000, 12, 206, 258, 6035, 16, 21963, 18, 14664, 540, 542, 22, 3165444, 424, 770, 6434, 53384, 28, 544568, 30, 1403235, 1416, 1346, 1718, 225979931, 36, 1694, 2010, 65907940, 40, 2493140, 42, 301152, 860064, 2510, 46, 112291412012, 1812

Offset: 1

Author

Wesley Ivan Hurt, Jun 12 2021

Keywords

• nonn

Comments

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

Examples

			a(10) = Sum_{d|10} (10-d)^tau(d) = 9^1 + 8^2 + 5^2 + 0^4 = 9 + 64 + 25 = 98.
		

Crossrefs

Cf. A000005 (tau), A174937.

Programs

Mathematica

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