A345271 a(n) = Sum_{d|n} n^tau(d).

1, 6, 12, 84, 30, 1374, 56, 4680, 819, 10210, 132, 3008748, 182, 38822, 51090, 1118480, 306, 34123698, 380, 64168820, 195384, 235246, 552, 110267095704, 16275, 458354, 551880, 482528508, 870, 656102432730, 992, 1108378656, 1188132, 1338682, 1503110, 101564312008644

Offset: 1

Author

Wesley Ivan Hurt, Jun 12 2021

Keywords

• nonn

Comments

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

Examples

			a(10) = Sum_{d|10} 10^tau(d) = 10^1 + 10^2 + 10^2 + 10^4 = 10210.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005 (tau), A174937, A345270, A345895.

Programs

Mathematica

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

PARI

a(n) = sumdiv(n, d, n^numdiv(d)); \\ Michel Marcus, Oct 08 2021