A291900 Sum of the divisors of 24*n - 1, divided by 24, minus n.

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, 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, 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

Offset: 1

Author

Omar E. Pol, Nov 02 2017

Keywords

• nonn
• easy

Comments

The indices of the zeros give A131210.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

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

PARI

a(n) = sigma(24*n-1)/24 - n; \\ Michel Marcus, Nov 04 2017

Formula

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

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