A015759 - OEIS

%I #26 Jan 08 2025 12:46:47

%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 an 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 [e.g., 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,changed

%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