A365446 Partial sums of A224613.

12, 40, 79, 139, 211, 302, 398, 522, 642, 810, 954, 1149, 1317, 1541, 1775, 2027, 2243, 2523, 2763, 3123, 3435, 3771, 4059, 4462, 4834, 5226, 5589, 6069, 6429, 6975, 7359, 7867, 8335, 8839, 9415, 10015, 10471, 11031, 11577, 12321, 12825, 13553, 14081, 14801, 15521, 16193, 16769, 17588, 18272, 19140, 19842

Offset

1,1

Comments

Partial sums of the sum of the divisors of the nonzero multiples of 6.

Links

Table of n, a(n) for n=1..51.

Formula

a(n) = (55*Pi^2/72) * n^2 + O(n*log(n)). - Amiram Eldar, Sep 07 2023

Mathematica

Accumulate[Table[DivisorSigma[1, 6*n], {n, 1, 50}]] (* Amiram Eldar, Sep 07 2023 *)

Prog

(Python)
from math import prod
from collections import Counter
from sympy import factorint
def A365446(n): return sum(prod((p**(e+1)-1)//(p-1) for p, e in (Counter(factorint(m))+Counter([2, 3])).items()) for m in range(1, n+1)) # Chai Wah Wu, Sep 07 2023

Crossrefs

Cf. A008588, A224613, A363161.

Sequence in context: A353839 A175583 A109766 * A033586 A211786 A320252

Adjacent sequences: A365443 A365444 A365445 * A365447 A365448 A365449

Keyword

nonn,easy

Author

Omar E. Pol, Sep 04 2023

Status

approved