A099979 - OEIS

%I #23 Aug 07 2022 09:53:07

%S 5,21,50,85,130,210,250,341,455,546,610,850,850,1050,1300,1365,1450,

%T 1911,1810,2210,2500,2562,2650,3410,3255,3570,4100,4250,4210,5460,

%U 4810,5461,6100,6090,6500,7735,6850,7602,8500,8866,8410,10500,9250,10370

%N Bisection of A001157: sigma_2(2n).

%H Seiichi Manyama, <a href="/A099979/b099979.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A001157(2*n) = sigma_2(2*n).

%F Sum_{k=1..n} a(k) ~ 3 * zeta(3) * n^3 / 2. - _Vaclav Kotesovec_, Aug 07 2022

%e a(1) = sigma_2(2*1) = 1 + 2^2 = 5.

%e a(2) = sigma_2(2*2) = 1 + 2^2 + 4^2 = 21.

%p with(numtheory): seq(sigma[2](2*n),n=1..50); # C. Ronaldo

%t Table[DivisorSigma[2,2n],{n,1,47}] (* _Indranil Ghosh_, Mar 03 2017 *)

%o (PARI) a(n) = sigma(2*n,2); \\ _Indranil Ghosh_, Mar 03 2017

%Y Sigma_2(k*n): A001157 (k=1), this sequence (k=2), A283237 (k=3).

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Nov 19 2004

%E More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 18 2005

%E Offset changed to 1 by _Seiichi Manyama_, Mar 03 2017

%E Examples added and name edited by _M. F. Hasler_, Mar 06 2017