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a(n) = sigma(3*n) = A000203(3*n).
18

%I #19 Dec 16 2022 09:04:33

%S 4,12,13,28,24,39,32,60,40,72,48,91,56,96,78,124,72,120,80,168,104,

%T 144,96,195,124,168,121,224,120,234,128,252,156,216,192,280,152,240,

%U 182,360,168,312,176,336,240,288,192,403,228,372,234,392,216,363,288,480,260,360

%N a(n) = sigma(3*n) = A000203(3*n).

%H Seiichi Manyama, <a href="/A144613/b144613.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000203(n) + 3*A078708(n). - _R. J. Mathar_, May 19 2020

%F Sum_{k=1..n} a(k) = (11*Pi^2/36) * n^2 + O(n*log(n)). - _Amiram Eldar_, Dec 16 2022

%t a[n_] := DivisorSigma[1, 3*n]; Array[a, 60] (* _Amiram Eldar_, Dec 16 2022 *)

%o (PARI) vector(66, n, sigma(3*n, 1)) \\ _Joerg Arndt_, Jul 30 2011

%Y Sigma(k*n): A000203 (k=1), A062731 (k=2), this sequence (k=3), A193553 (k=4), A283118 (k=5), A224613 (k=6), A283078 (k=7), A283122 (k=8), A283123 (k=9).

%Y Cf. A008585, A078708.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Jan 15 2009

%E Zero removed and offset corrected by Seiichi Manyama, Feb 28 2017