A372709 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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));