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a(n) = Chowla's function of n * sigma(n).
1

%I #28 Apr 01 2024 02:35:54

%S 0,0,0,14,0,60,0,90,39,126,0,420,0,216,192,434,0,780,0,882,320,468,0,

%T 2100,155,630,480,1512,0,2952,0,1890,672,1026,576,4914,0,1260,896,

%U 4410,0,5088,0,3276,2496,1800,0,9300,399,3906,1440,4410,0,7800,1152,7560,1760,2790,0,17976,0,3168,4160,7874,1512

%N a(n) = Chowla's function of n * sigma(n).

%H Amiram Eldar, <a href="/A062785/b062785.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)

%F a(n) = A000203(n)*A048050(n). - _Michel Marcus_, Jun 29 2018

%F Sum_{k=1..n} a(k) ~ (5*zeta(3)/6 - Pi^2/18) * n^3. - _Amiram Eldar_, Apr 01 2024

%t a[n_] := Module[{s = DivisorSigma[1, n]}, s*(s - n - 1)]; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Apr 01 2024 *)

%o (PARI) a(n) = {my(s = sigma(n)); if(n == 1, 0, s*(s-n-1));}

%Y Cf. A000203, A048050.

%Y Cf. A002117, A086463.

%K easy,nonn

%O 1,4

%A _Jason Earls_, Jul 18 2001

%E a(1) corrected by _Amiram Eldar_, Apr 01 2024