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A365446
Partial sums of A224613.
4
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.
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
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 04 2023
STATUS
approved