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

%I A077089 #20 Mar 18 2025 04:15:50
%S A077089 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,
%T A077089 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,
%U A077089 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
%N A077089 Quotients when sigma(k+1)/sigma(k) is an integer.
%H A077089 Amiram Eldar, <a href="/A077089/b077089.txt">Table of n, a(n) for n = 1..5000</a> (terms 1..500 from Seiichi Manyama)
%F A077089 a(n) = sigma(A058072(n)+1)/sigma(A058072(n)). - _Seiichi Manyama_, Jan 16 2021
%e A077089 a(1) = sigma(2)/sigma(1) = 3/1 = 3.
%e A077089 a(2) = sigma(6)/sigma(5) = 12/6 = 2.
%e A077089 a(3) = sigma(15)/sigma(14) = 24/24 = 1.
%t A077089 Do[s=Mod[a=DivisorSigma[1, n+1], b=DivisorSigma[1, n]]; If[Equal[s, 0], Print[a/b]], {n, 1, 10000000}]
%t A077089 Select[#[[2]]/#[[1]]&/@Partition[DivisorSigma[1,Range[10^6]],2,1], IntegerQ] (* _Harvey P. Dale_, Dec 26 2015 *)
%Y A077089 Cf. A000203, A002961, A058072, A067081, A077086, A077087.
%K A077089 nonn
%O A077089 1,1
%A A077089 _Labos Elemer_, Oct 31 2002