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.
%I A076487 #21 Jul 19 2024 19:39:29
%S A076487 1,2,3,4,5,6,7,8,10,11,13,14,15,16,17,19,20,21,22,23,26,27,29,30,31,
%T A076487 32,33,34,35,37,38,39,40,41,42,43,46,47,51,53,55,57,58,59,60,61,62,63,
%U A076487 64,65,66,67,68,69,70,71,73,74,77,78,79,80,82,83,85,86,87,89,91,93,94,95
%N A076487 Solutions to gcd(sigma(x), phi(x)) = gcd(sigma(core(x)), phi(core(x))), i.e., when A009223(x) = A066086(x) or if A066087(x) = 0.
%C A076487 The squarefree numbers are a subset of this sequence.
%H A076487 Amiram Eldar, <a href="/A076487/b076487.txt">Table of n, a(n) for n = 1..10000</a>
%e A076487 For n=20: sigma(20)=42, phi(20)=8, gcd(42,8)=2, core(20)=10, sigma(10)=18, phi(10)=4, gcd(18,4)=2, so A009223(20) = A066086(20)=2.
%t A076487 ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] cor[x_] := Apply[Times, ba[x]] g1[x_] := GCD[DivisorSigma[1, x], EulerPhi[x]] g2[x_] := GCD[DivisorSigma[1, cor[x]], EulerPhi[cor[x]]] Do[s1=g1[n]; s2=g2[n]; If[Equal[s2, s1], Print[n]], {n, 1, 256}]
%o A076487 (PARI) isok(n) = my(c=core(n)); gcd(sigma(n), eulerphi(n)) == gcd(sigma(c), eulerphi(c)); \\ _Michel Marcus_, Jul 30 2017
%Y A076487 Cf. A000010, A000203, A007947, A009223, A023900, A048250, A066086, A066087, A076485, A076486.
%K A076487 nonn
%O A076487 1,2
%A A076487 _Labos Elemer_, Oct 17 2002