A092348 - OEIS

%I #22 Jan 02 2025 07:55:10

%S 0,6,24,66,120,240,336,570,744,1116,1320,2016,2184,3072,3504,4650,

%T 4896,6774,6840,9156,9600,11952,12144,16320,15720,19740,20400,25056,

%U 24360,31680,29760,37386,37248,44172,43296,55170,50616,61680,61488,73620,68880,86592

%N a(n) = sigma_3(n) - sigma_1(n).

%H Seiichi Manyama, <a href="/A092348/b092348.txt">Table of n, a(n) for n = 1..10000</a>

%F G.f.: Sum_{k>=1} k*(k^2 - 1)*x^k/(1 - x^k). - _Ilya Gutkovskiy_, Mar 17 2017

%F G.f.: 6 * Sum_{k>0} x^(2*k)/(1-x^k)^4. - _Seiichi Manyama_, Jun 11 2023

%F From _Amiram Eldar_, Jan 01 2025: (Start)

%F Dirichlet g.f.: zeta(s) * (zeta(s-3) - zeta(s-1)).

%F Sum_{k=1..n} a(k) ~ (zeta(4)/4) * n^4. (End)

%t a[n_] := Subtract @@ DivisorSigma[{3, 1}, n]; Array[a, 50] (* _Amiram Eldar_, Jan 01 2025 *)

%o (PARI) a(n) = sigma(n, 3)-sigma(n); \\ _Seiichi Manyama_, Jun 11 2023

%Y Cf. A000203, A001158, A013662.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Mar 20 2004