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a(0)=1; a(n) = sigma_1(n) + sigma_3(n).
2

%I #11 Apr 14 2021 15:18:34

%S 1,2,12,32,80,132,264,352,600,770,1152,1344,2072,2212,3120,3552,4712,

%T 4932,6852,6880,9240,9664,12024,12192,16440,15782,19824,20480,25168,

%U 24420,31824,29824,37512,37344,44280,43392,55352,50692,61800,61600,73800,68964,86784

%N a(0)=1; a(n) = sigma_1(n) + sigma_3(n).

%H Harvey P. Dale, <a href="/A092345/b092345.txt">Table of n, a(n) for n = 0..1000</a>

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

%t nxt[{n_,a_}]:={n+1,DivisorSigma[1,n+1]+DivisorSigma[3,n+1]}; NestList[nxt,{0,1},50][[All,2]] (* _Harvey P. Dale_, Apr 14 2021 *)

%Y Cf. A000203, A001158.

%K nonn

%O 0,2

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