A344579 a(n) = Sum_{d|n} d^sopf(d).

1, 5, 28, 21, 3126, 7808, 823544, 85, 757, 10003130, 285311670612, 256656, 302875106592254, 20661870332, 2562893778, 341, 827240261886336764178, 1898105, 1978419655660313589123980, 1290003146, 16679881801772, 282810343194753368, 20880467999847912034355032910568, 8219344

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..24.

Example

a(6) = Sum_{d|6} d^sopf(d) = 1^0 + 2^2 + 3^3 + 6^5 = 7808.

Mathematica

Table[Sum[i^Sum[k (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[i/k] + Floor[i/k]), {k, i}] (1 - Ceiling[n/i] + Floor[n/i]), {i, n}], {n, 30}]

Crossrefs

Cf. A008472 (sopf), A344578.

Sequence in context: A347251 A321236 A351774 * A345263 A218346 A106679

Adjacent sequences: A344576 A344577 A344578 * A344580 A344581 A344582

Keyword

nonn

Author

Wesley Ivan Hurt, May 23 2021

Status

approved