cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A073808 Number of common divisors of sigma_1(n) and sigma_2(n).

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%I A073808 #16 Nov 23 2017 21:36:42
%S A073808 1,1,2,2,2,2,2,2,2,2,2,4,2,2,3,2,2,2,2,8,3,2,2,4,2,2,6,4,2,3,2,4,3,2,
%T A073808 3,4,2,4,3,4,2,3,2,8,4,2,2,4,4,4,3,4,2,6,3,4,6,4,2,12,2,2,4,2,3,3,2,8,
%U A073808 3,3,2,4,2,2,4,4,3,3,2,4,3,2,2,6,3,2,6,4,2,4,3,8,3,2,3,8,2,4,4,4,2,3,2,4
%N A073808 Number of common divisors of sigma_1(n) and sigma_2(n).
%C A073808 a(n) = Card[Intersection[D[A000203(n)], D[A001157(n)]]]. - This is the formula given by the original author. D[x] here means the set of divisors of x. - _Antti Karttunen_, Nov 23 2017
%H A073808 Antti Karttunen, <a href="/A073808/b073808.txt">Table of n, a(n) for n = 1..16384</a>
%F A073808 a(n) = A000005(gcd(A000203(n), A001157(n))). - _Antti Karttunen_, Nov 23 2017
%e A073808 n=10: sigma[1,10]=18, sigma[1,10]=130 Intersection[{1,2,3,6,9,18},{1,2,5,10,13,26,65,130}]={1,2}, so a(10)=2.
%t A073808 g1[x_] := Divisors[DivisorSigma[1, x]] g2[x_] := Divisors[DivisorSigma[2, x]] ncd[x_] := Length[Intersection[g1[x], g2[x]]] Table[ncd[w], {w, 1, 128}]
%t A073808 (* Second program: *)
%t A073808 Table[Length@ Apply[Intersection, Divisors@ Array[DivisorSigma[#, n] &, 2]], {n, 105}] (* _Michael De Vlieger_, Nov 23 2017 *)
%o A073808 (PARI) A073808(n) = numdiv(gcd(sigma(n),sigma(n,2))); \\ _Antti Karttunen_, Nov 23 2017
%Y A073808 Cf. A000005, A000203, A001157, A073802, A073809.
%K A073808 nonn
%O A073808 1,3
%A A073808 _Labos Elemer_, Aug 13 2002