This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A015713 #29 Feb 11 2024 02:37:49
%S A015713 4,9,18,49,81,98,121,162,242,361,529,722,729,961,1058,1458,1849,1922,
%T A015713 2209,2401,3481,3698,4418,4489,4802,5041,6241,6561,6889,6962,8978,
%U A015713 10082,10609,11449,12482,13122,13778,14641,16129,17161
%N A015713 Numbers m such that phi(m) * sigma(m) + k^2 is not a square for any k.
%C A015713 Numbers m such that A062354(m) is in A016825. - _Michel Marcus_, Dec 07 2018
%H A015713 Amiram Eldar, <a href="/A015713/b015713.txt">Table of n, a(n) for n = 1..10000</a>
%H A015713 Richard K. Guy, <a href="https://www.jstor.org/stable/2974586">Divisors and desires</a>, Amer. Math. Monthly, 104 (1997), 359-360.
%F A015713 Conjecture: {4, p^(2*m), 2*p^(2*m), p = 4*k+3 is prime}. - _Sean A. Irvine_, Dec 06 2018
%F A015713 The conjecture is true. It can be proved using the multiplicative property of A062354(n), i.e., A062354(p^e) = p^(e-1)*(p^(e+1)-1), and that if m is a term then A007814(A062354(m)) = 1. - _Amiram Eldar_, Feb 11 2024
%t A015713 nonSqDiffQ[n_] := Mod[n, 4] == 2; aQ[n_] := nonSqDiffQ[ EulerPhi[n] * DivisorSigma[ 1, n]]; Select[Range[20000], aQ] (* _Amiram Eldar_, Dec 07 2018 *)
%o A015713 (PARI) isok(n) = (sigma(n)*eulerphi(n) % 4) == 2; \\ _Michel Marcus_, Dec 07 2018
%Y A015713 Cf. A007814, A015710, A062354 (phi(n)*sigma(n)), A016825.
%K A015713 nonn
%O A015713 1,1
%A A015713 _Robert G. Wilson v_