A066293 - OEIS

%I #23 Mar 17 2024 03:15:26

%S 0,4,6,28,10,94,14,140,78,194,22,574,26,326,316,620,34,1066,38,1218,

%T 524,686,46,2750,310,914,780,2086,58,3884,62,2604,1084,1466,1004,6370,

%U 74,1790,1436,5890,82,6716,86,4494,3718,2534,94,11966,798,5394,2284

%N a(n) = A000203(n)^2 - A001157(n) = sigma(n)^2 - sigma_2(n).

%H Amiram Eldar, <a href="/A066293/b066293.txt">Table of n, a(n) for n = 1..10000</a>

%F For p prime, a(p) = 2p.

%F From _Amiram Eldar_, Mar 17 2024: (Start)

%F a(n) = A072861(n) - A001157(n).

%F Sum_{k=1..n} a(k) ~ c * n^3, where c = zeta(3)/2 = 0.601028451579... . (End)

%t a[n_] := DivisorSigma[1, n]^2 - DivisorSigma[2, n]; Array[a, 50] (* _Amiram Eldar_, Jul 31 2019 *)

%o (PARI) a(n) = sigma(n)^2 - sigma(n, 2); \\ _Michel Marcus_, Mar 22 2020

%Y Cf. A000203, A001157, A002117, A072861.

%K nonn

%O 1,2

%A _Labos Elemer_, Dec 12 2001