A291900 - OEIS

%I #38 Mar 28 2024 09:03:07

%S 0,0,0,1,1,1,0,0,2,0,0,2,0,3,0,0,2,0,9,0,0,2,2,7,0,4,0,3,6,0,0,3,5,7,

%T 0,0,0,0,15,6,0,3,0,9,4,0,10,0,13,5,0,3,3,22,0,4,0,5,12,0,19,0,0,13,0,

%U 0,0,10,14,4,6,7,5,19,11,0,0,0,16,5,4,12,8,28,0,0,0,0,35,6,4,0,5,32,4,18,8,0,31,0

%N Sum of the divisors of 24*n - 1, divided by 24, minus n.

%C The indices of the zeros give A131210.

%H Robert Israel, <a href="/A291900/b291900.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = sigma(24*n-1)/24 - n = A000203(A183010(n))/24 - n = A280097(n)/24 - n = A280098(n) - n.

%F Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/18 - 1/2 = 0.048311... . - _Amiram Eldar_, Mar 28 2024

%t a[n_] := DivisorSigma[1, 24 n - 1]/24 - n; Array[a, 90] (* _Robert G. Wilson v_, Nov 04 2017 *)

%o (PARI) a(n) = sigma(24*n-1)/24 - n; \\ _Michel Marcus_, Nov 04 2017

%Y Cf. A000203, A008606, A086463, A131210, A134517, A183010, A183011, A280097, A280098, A294614.

%K nonn,easy

%O 1,9

%A _Omar E. Pol_, Nov 02 2017