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A179879 Numbers h such that h and h+1 have same antiharmonic mean of the numbers k < h such that gcd(k, h) = 1 and simultaneously this mean is not integer.

%I A179879 #13 May 25 2025 01:42:42
%S A179879 6,65,69,77,129,185,194,210,221,237,254,309,321,330,365,398,417,437,
%T A179879 462,473,482,497,533,546,554,570,573,581,597,614,626,662,669,681,690,
%U A179879 714,753,758,785,789,794,813,858,893,905,914,966,993,1037,1073,1094,1101,1122
%N A179879 Numbers h such that h and h+1 have same antiharmonic mean of the numbers k < h such that gcd(k, h) = 1 and simultaneously this mean is not integer.
%C A179879 Subsequence of A179875 and A179883.
%C A179879 For corresponding values of numbers h+1 see A179880. - _Jaroslav Krizek_, Jul 31 2010
%H A179879 Amiram Eldar, <a href="/A179879/b179879.txt">Table of n, a(n) for n = 1..10000</a>
%F A179879 a(n) = A179880(n) - 1. - _Jaroslav Krizek_, Jul 31 2010
%o A179879 (PARI) ah(n) = {my(f = factor(n)); if(n == 1, 1, 2*n/3 + (1/3) * prod(i = 1, #f~, 1 - f[i, 1])/eulerphi(f));}
%o A179879 isok(k) = {my(ah1 = ah(k), ah2 = ah(k+1)); ah1 == ah2 && denominator(ah1) > 1;} \\ _Amiram Eldar_, May 24 2025
%Y A179879 Cf. A179871, A179872, A179873, A179874, A179875, A179876, A179877, A179878, A179880, A179882, A179883, A179884, A179885, A179886, A179887, A179890, A179891.
%K A179879 nonn
%O A179879 1,1
%A A179879 _Jaroslav Krizek_, Jul 30 2010
%E A179879 a(36) corrected and more terms added by _Amiram Eldar_, May 24 2025