A372709 a(n) = Sum_{k=1..n} tau(n*k), where tau(n) = number of divisors of n, cf. A000005.

1, 5, 9, 18, 19, 41, 31, 56, 59, 83, 57, 136, 73, 127, 151, 170, 103, 233, 119, 270, 239, 233, 151, 406, 241, 285, 311, 424, 205, 579, 225, 464, 425, 399, 473, 758, 283, 459, 517, 812, 319, 891, 339, 742, 853, 587, 375, 1138, 571, 893, 731, 920, 437, 1157, 847, 1250

Offset

1,2

Links

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

Vaclav Kotesovec, Plot of a(n) / A372674(n) for n = 1..100000

Formula

Conjecture: a(n) ~ A372674(n) / 2. - Vaclav Kotesovec, May 13 2024

Mathematica

Table[Sum[DivisorSigma[0, k*n], {k, 1, n}], {n, 1, 50}] (* Vaclav Kotesovec, May 13 2024 *)

Prog

(PARI) a(n) = sum(k=1, n, numdiv(n*k));

Crossrefs

Cf. A000005, A048691, A263086, A372674, A372710.

Sequence in context: A233584 A262315 A315119 * A061502 A110349 A036832

Adjacent sequences: A372706 A372707 A372708 * A372710 A372711 A372712

Keyword

nonn

Author

Seiichi Manyama, May 11 2024

Status

approved