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.

A047727 Average divisor is an integer (A003601) and the number is refactorable (A033950).

This page as a plain text file.
%I A047727 #22 Oct 18 2016 05:39:47
%S A047727 1,56,60,96,132,184,204,248,276,348,376,480,492,504,564,568,612,632,
%T A047727 636,672,708,824,852,864,996,1016,1056,1068,1208,1212,1248,1284,1336,
%U A047727 1356,1520,1528,1572,1592,1632,1644,1656,1784,1788,1824,1908,1912,1980
%N A047727 Average divisor is an integer (A003601) and the number is refactorable (A033950).
%H A047727 Donovan Johnson, <a href="/A047727/b047727.txt">Table of n, a(n) for n = 1..10000</a>
%F A047727 Both sigma_1(x)/sigma_0(x) and x/sigma_0(x) are integers. - clarified by _Harvey P. Dale_, Apr 27 2012
%e A047727 x = 56, sigma(x) = 120, number of divisors of x = 8. 120/8 and 56/8 are integers.
%t A047727 adiQ[n_]:=Module[{ds1=DivisorSigma[1,n],ds0=DivisorSigma[0,n]} ,Divisible[ ds1,ds0]&&Divisible[n,ds0]]; Select[Range[2000],adiQ] (* _Harvey P. Dale_, Apr 27 2012 *)
%o A047727 (PARI) isok(n) = my(d = numdiv(n)); !(n % d) && !(sigma(n) % d); \\ _Michel Marcus_, Oct 15 2016
%Y A047727 Cf. A007691, A001599, A046985.
%K A047727 nonn
%O A047727 1,2
%A A047727 _Labos Elemer_