A365446 - OEIS

%I #21 Sep 07 2023 16:06:48

%S 12,40,79,139,211,302,398,522,642,810,954,1149,1317,1541,1775,2027,

%T 2243,2523,2763,3123,3435,3771,4059,4462,4834,5226,5589,6069,6429,

%U 6975,7359,7867,8335,8839,9415,10015,10471,11031,11577,12321,12825,13553,14081,14801,15521,16193,16769,17588,18272,19140,19842

%N Partial sums of A224613.

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

%F a(n) = (55*Pi^2/72) * n^2 + O(n*log(n)). - _Amiram Eldar_, Sep 07 2023

%t Accumulate[Table[DivisorSigma[1, 6*n], {n, 1, 50}]] (* _Amiram Eldar_, Sep 07 2023 *)

%o (Python)

%o from math import prod

%o from collections import Counter

%o from sympy import factorint

%o 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

%Y Cf. A008588, A224613, A363161.

%K nonn,easy

%O 1,1

%A _Omar E. Pol_, Sep 04 2023