A077089 Quotients when sigma(k+1)/sigma(k) is an integer.

3, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 3, 1, 3, 1, 2, 1, 2, 2, 3, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2, 2, 2, 3, 1, 2, 2, 3, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 3, 2, 2, 1, 2, 2, 1, 2, 3, 3, 1, 3, 1, 2, 2, 2, 3, 2, 1, 1, 3, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 3, 3, 2, 1, 2, 1, 2, 2, 3, 1, 2, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Labos Elemer, Oct 31 2002

Keywords

• nonn

Examples

			a(1) = sigma(2)/sigma(1) = 3/1 = 3.
a(2) = sigma(6)/sigma(5) = 12/6 = 2.
a(3) = sigma(15)/sigma(14) = 24/24 = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..5000 (terms 1..500 from Seiichi Manyama)

Crossrefs

Cf. A000203, A002961, A058072, A067081, A077086, A077087.

Programs

Mathematica

Do[s=Mod[a=DivisorSigma[1, n+1], b=DivisorSigma[1, n]]; If[Equal[s, 0], Print[a/b]], {n, 1, 10000000}]
Select[#[[2]]/#[[1]]&/@Partition[DivisorSigma[1,Range[10^6]],2,1], IntegerQ] (* Harvey P. Dale, Dec 26 2015 *)

Formula

a(n) = sigma(A058072(n)+1)/sigma(A058072(n)). - Seiichi Manyama, Jan 16 2021