A344458 a(n) = Sum_{d|n} d^omega(d).

1, 3, 4, 7, 6, 42, 8, 15, 13, 108, 12, 190, 14, 206, 234, 31, 18, 375, 20, 512, 452, 498, 24, 774, 31, 692, 40, 994, 30, 27372, 32, 63, 1104, 1176, 1238, 1819, 38, 1466, 1538, 2120, 42, 74774, 44, 2438, 2268, 2142, 48, 3094, 57, 2633, 2622, 3400, 54, 3318, 3042, 4138

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..56.

Example

a(6) = Sum_{d|6} d^omega(d) = 1^0 + 2^1 + 3^1 + 6^2 = 42.

Mathematica

Table[Sum[k^PrimeNu[k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]

Crossrefs

Cf. A001221 (omega).

Sequence in context: A334127 A095001 A377378 * A068905 A241625 A081826

Adjacent sequences: A344455 A344456 A344457 * A344459 A344460 A344461

Keyword

nonn

Author

Wesley Ivan Hurt, May 19 2021

Status

approved