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

Author

Labos Elemer, Oct 31 2002

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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