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A347891 Odd numbers k such that sigma(k^2) > 2*k^2 and A003415(sigma(k^2)) < k^2.

%I A347891 #8 Sep 19 2021 22:03:02
%S A347891 495,735,945,1485,1755,2205,2475,2625,2805,3315,3675,3795,4455,4785,
%T A347891 4845,5145,5265,5445,6615,6765,7425,7605,7755,8085,8415,8505,8745,
%U A347891 8775,9735,11025,12375,12495,13365,13965,14025,15435,15795,16065,16335,16905,17595,18375,19845,20295,21315,22185,22275,22785,22815,23265
%N A347891 Odd numbers k such that sigma(k^2) > 2*k^2 and A003415(sigma(k^2)) < k^2.
%C A347891 Odd numbers whose square is abundant and present in A343216.
%C A347891 The first term that is not a multiple of 5 is a(146) = 82467.
%H A347891 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A347891 a(n) = A000196(A347890(n)).
%t A347891 ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[1, 24000, 2], DivisorSigma[1, #^2] > 2*#^2 && ad[DivisorSigma[1, #^2]] < #^2 &] (* _Amiram Eldar_, Sep 19 2021 *)
%o A347891 (PARI)
%o A347891 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A347891 isA347891(n) = if(!(n%2),0,my(u=n*n); (A003415(sigma(u))<u)&&(sigma(u)>(2*u)));
%Y A347891 Square roots of A347890. Subsequence of A174830.
%Y A347891 Cf. A000196, A000203, A003415, A005231, A343216.
%K A347891 nonn
%O A347891 1,1
%A A347891 _Antti Karttunen_, Sep 19 2021