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

1,9

Comments

The indices of the zeros give A131210.

Links

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

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A143068 A261202 A334596 * A263146 A365047 A361015

Adjacent sequences: A291897 A291898 A291899 * A291901 A291902 A291903

Keyword

nonn,easy

Author

Omar E. Pol, Nov 02 2017

Status

approved