A077086 Remainder when sigma(n+1) is divided by sigma(n).

0, 1, 3, 6, 0, 8, 7, 13, 5, 12, 4, 14, 10, 0, 7, 18, 3, 20, 2, 32, 4, 24, 12, 31, 11, 40, 16, 30, 12, 32, 31, 48, 6, 48, 43, 38, 22, 56, 34, 42, 12, 44, 40, 78, 72, 48, 28, 57, 36, 72, 26, 54, 12, 72, 48, 80, 10, 60, 48, 62, 34, 8, 23, 84, 60, 68, 58, 96, 48, 72, 51, 74, 40, 10

Offset

1,3

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

a(n) = Mod(A000203(n+1), A000203(n)).

Example

a(7) = 7 since sigma(7) = 8, sigma(8) = 15, and 15 = 1*8 + 7.

Mathematica

a[n_]:=Mod[DivisorSigma[1, n+1], DivisorSigma[1, n]]; Array[a, 74] (* Stefano Spezia, Jan 24 2025 *)

Prog

(PARI) a(n) = sigma(n+1) % sigma(n); \\ Michel Marcus, Dec 26 2013

Crossrefs

Cf. A000203, A000668 (fixed points), A002961, A067081.

Sequence in context: A200005 A153097 A271854 * A010618 A378800 A287845

Adjacent sequences: A077083 A077084 A077085 * A077087 A077088 A077089

Keyword

nonn

Author

Labos Elemer, Oct 31 2002

Status

approved