%I
%S 1,2,3,6,22,33,66,750,27798250,41697375,76745867,83394750,153491734,
%T 207656250,230237601,460475202,917342250,969062500,2907187500,
%U 4528006153,5952812500,9056012306,13584018459,17858437500,27168036918,31979062500,57559400250
%N Numbers k such that phi(k)  sigma_2(k).
%C sigma_2(k) is the sum of the squares of the divisors of k (A001157).
%C All of these terms are solutions to relations for all j as follows: {sigma(j,x)/phi(x) is integer for exponents j=4k+2}. Proof is possible by individual managements in the knowledge of divisors of x and phi(x). Compare with A015765, A015768, etc.  _Labos Elemer_, May 25 2004
%t Do[ If[ IntegerQ[ DivisorSigma[2, n]/EulerPhi[n]], Print[n]], {n, 1, 10^7}]
%t Empirical test for very high power sums of divisors [eg d^2802..]. Table[{4*j+2, Union[Table[IntegerQ[DivisorSigma[4*j+2, Part[t, k]]/EulerPhi[Part[t, k]]], {k, 1, 13}]]}, {j, 0, 700}] Output = {True} for all 4j+2. Here t=A015759. (* _Labos Elemer_, May 20 2004 *)
%Y Cf. A000010, A001157, A093643.
%Y Cf. A015765, A015768, A094470.
%K nonn
%O 1,2
%A _Robert G. Wilson v_
%E a(9)a(13) from _Labos Elemer_, May 20 2004
%E a(14)a(18) from _Donovan Johnson_, Feb 05 2010
%E a(19)a(27) from _Donovan Johnson_, Jun 18 2011
