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

Author

Seiichi Manyama, May 11 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000
• Vaclav Kotesovec, Plot of a(n) / A372674(n) for n = 1..100000

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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