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A065150 Numbers k such that the harmonic mean of phi(k) and sigma(k) is an integer. 1

%I

%S 1,12,15,35,56,78,95,140,143,172,190,248,264,287,315,319,323,357,418,

%T 477,588,594,675,812,814,840,899,910,1045,1107,1118,1131,1199,1208,

%U 1254,1349,1420,1425,1485,1495,1558,1608,1672,1763,2214,2261,2318,2337

%N Numbers k such that the harmonic mean of phi(k) and sigma(k) is an integer.

%H Harry J. Smith, <a href="/A065150/b065150.txt">Table of n, a(n) for n = 1..1000</a>

%F G^2 mod A = 0, where G^2 = A000010(m)*A000203(m), A = (A000010(m) + A000203(m))/2; harmonic mean = (G^2)/A is integer.

%e 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.

%o (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 Cf. A000010, A000203, A065146, A011257.

%K nonn

%O 1,2

%A _Labos Elemer_, Oct 18 2001

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Last modified May 9 05:11 EDT 2021. Contains 343688 sequences. (Running on oeis4.)