A092348 a(n) = sigma_3(n) - sigma_1(n).
0, 6, 24, 66, 120, 240, 336, 570, 744, 1116, 1320, 2016, 2184, 3072, 3504, 4650, 4896, 6774, 6840, 9156, 9600, 11952, 12144, 16320, 15720, 19740, 20400, 25056, 24360, 31680, 29760, 37386, 37248, 44172, 43296, 55170, 50616, 61680, 61488, 73620, 68880, 86592
Offset: 1
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..10000
Programs
-
Mathematica
a[n_] := Subtract @@ DivisorSigma[{3, 1}, n]; Array[a, 50] (* Amiram Eldar, Jan 01 2025 *) -
PARI
a(n) = sigma(n, 3)-sigma(n); \\ Seiichi Manyama, Jun 11 2023
Formula
G.f.: Sum_{k>=1} k*(k^2 - 1)*x^k/(1 - x^k). - Ilya Gutkovskiy, Mar 17 2017
G.f.: 6 * Sum_{k>0} x^(2*k)/(1-x^k)^4. - Seiichi Manyama, Jun 11 2023
From Amiram Eldar, Jan 01 2025: (Start)
Dirichlet g.f.: zeta(s) * (zeta(s-3) - zeta(s-1)).
Sum_{k=1..n} a(k) ~ (zeta(4)/4) * n^4. (End)