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 A065150 #23 Mar 20 2025 03:23:14
%S A065150 1,12,15,35,56,78,95,140,143,172,190,248,264,287,315,319,323,357,418,
%T A065150 477,588,594,675,812,814,840,899,910,1045,1107,1118,1131,1199,1208,
%U A065150 1254,1349,1420,1425,1485,1495,1558,1608,1672,1763,2214,2261,2318,2337
%N A065150 Numbers k such that the harmonic mean of phi(k) and sigma(k) is an integer.
%H A065150 Amiram Eldar, <a href="/A065150/b065150.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)
%F A065150 G^2 mod A = 0, where G^2 = A000010(m)*A000203(m), A = (A000010(m) + A000203(m))/2; harmonic mean = (G^2)/A is an integer.
%e A065150 m = 319, phi(319) = 280, sigma(319) = 360; phi(319)*sigma(319) = 100800, phi(319) + sigma(319) = 640; 1/(harmonic mean) = (640/100800)/2, harmonic mean = 315, arithmetic mean = 320, geometric mean is not an integer.
%t A065150 Select[Range[2400], IntegerQ[HarmonicMean @ {EulerPhi[#], DivisorSigma[1, #]}] &] (* _Amiram Eldar_, Mar 20 2025 *)
%o A065150 (PARI) { n=0; for (m=1, 10^9, e=eulerphi(m); s=sigma(m); h=(2*e*s)/(e + s); if (frac(h) == 0, write("b065150.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Oct 13 2009
%Y A065150 Cf. A000010, A000203, A065146, A011257.
%K A065150 nonn
%O A065150 1,2
%A A065150 _Labos Elemer_, Oct 18 2001