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A293391 Integers n such that sigma(n)/phi(n) is a perfect square.

%I A293391 #37 Jan 14 2024 12:11:13
%S A293391 1,14,30,105,248,264,418,714,1485,3080,3135,3596,3828,3956,4064,5396,
%T A293391 6678,8636,10098,12648,20026,20790,21318,22152,23374,24882,25714,
%U A293391 26040,35074,35343,39105,41656,43890,44660,49938,55154,56134,56536,61344,71145,74613,86304,87087,94944
%N A293391 Integers n such that sigma(n)/phi(n) is a perfect square.
%C A293391 From _Robert Israel_, Dec 12 2017: (Start)
%C A293391 Intersection of A011257 and A020492.
%C A293391 If x and y are coprime members of the sequence, then x*y is in the sequence.
%C A293391 Contains all members of A133028 except 3. (End)
%H A293391 Giovanni Resta, <a href="/A293391/b293391.txt">Table of n, a(n) for n = 1..10000</a> (first 349 terms from Robert Israel)
%H A293391 J. A. B. Dris and C. Leibovici, <a href="https://math.stackexchange.com/q/2462552">Why is this sequence not in the OEIS?</a>, October 8 2017.
%H A293391 ProofWiki, <a href="https://proofwiki.org/wiki/Integers_whose_Ratio_between_Sigma_and_Phi_is_Square">Integers whose ratio between sigma and phi is square</a>, misses the second term, 14 as of Dec 2017.
%F A293391 a(n) = sigma(n)/phi(n) = m^2, for some integer m.
%e A293391 sigma(14)=3*8=24, phi(14)=14*(1/2)*(6/7)=6, sigma(14)/phi(14)=2^2, so 14 is in the list.
%p A293391 for n from 1 to 100000 do
%p A293391     r := numtheory[sigma](n)/numtheory[phi](n) ;
%p A293391     if issqr(r) then
%p A293391         printf("%d,",n) ;
%p A293391     end if;
%p A293391 end do: # _R. J. Mathar_, Dec 07 2017
%t A293391 Select[Range[10^5], IntegerQ@ Sqrt[DivisorSigma[1, #]/EulerPhi[#]] &] (* _Michael De Vlieger_, Dec 08 2017 *)
%o A293391 (PARI) isok(n) = my(q=sigma(n)/eulerphi(n)); issquare(q) && (denominator(q) == 1); \\ _Michel Marcus_, Dec 07 2017; corrected Sep 21 2019
%Y A293391 Cf. A000010, A000203, A011257, A020492, A133028, A289336, A289412, A292422.
%K A293391 nonn
%O A293391 1,2
%A A293391 _Jose Arnaldo Bebita Dris_, Oct 08 2017