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%I #14 Mar 11 2020 06:12:30
%S 2,18,21,99,133,151,175,183,350,366,449,450,477,532,581,645,702,843,
%T 1072,1253,1346,1508,1645,1833,2085,2097,2150,2421,3668,3950,4223,
%U 4312,4453,5264,6601,6853,7128,7423,7622,7713,8325,9028,9364,9707,10820
%N Numbers k such that sigma(phi(k))-phi(sigma(k)) is nonzero and divisible by phi(k), that is A065395(k)/A000010(k) is a nonzero integer.
%H Amiram Eldar, <a href="/A092587/b092587.txt">Table of n, a(n) for n = 1..10000</a>
%e (sigma(phi(x))-phi(sigma(x)))/phi(x) quotient equals -3 for x=450, -2 for x=18, -1 for x=2, 1 for x=21, 2 for x=99, 3 for x=4223.
%t fs[x_] := EulerPhi[DivisorSigma[1, x]] sf[x_] := DivisorSigma[1, EulerPhi[x]] {t=Table[0, {60}], j=1}; Do[s=(sf[n]-fs[n])/EulerPhi[n]; If[ !Equal[s, 0]&&IntegerQ[s], Print[n];t[[j]]=n;j=j+1], {n, 2, 1000000}] t
%Y Cf. A000010, A000203, A033632, A065395, A092584-A092588.
%K nonn
%O 1,1
%A _Labos Elemer_, Mar 01 2004