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A179880 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 A179880 #16 May 25 2025 01:40:05
%S A179880 7,66,70,78,130,186,195,211,222,238,255,310,322,331,366,399,418,438,
%T A179880 463,474,483,498,534,547,555,571,574,582,598,615,627,663,670,682,691,
%U A179880 715,754,759,786,790,795,814,859,894,906,915,967,994,1038,1074,1095,1102,1123
%N A179880 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 A179880 Subsequence of A179876 and A179883.
%C A179880 For corresponding values of numbers h-1 see A179879. - _Jaroslav Krizek_, Jul 31 2010
%H A179880 Amiram Eldar, <a href="/A179880/b179880.txt">Table of n, a(n) for n = 1..10000</a>
%F A179880 a(n) = A179879(n) + 1. - _Jaroslav Krizek_, Jul 31 2010
%o A179880 (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 A179880 isok(k) = {if( k == 1, 0, my(ah1 = ah(k), ah2 = ah(k-1)); ah1 == ah2 && denominator(ah1) > 1);} \\ _Amiram Eldar_, May 24 2025
%Y A179880 Cf. A179871, A179872, A179873, A179874, A179875, A179876, A179877, A179878, A179879, A179882, A179883, A179884, A179885, A179886, A179887, A179890, A179891.
%K A179880 nonn
%O A179880 1,1
%A A179880 _Jaroslav Krizek_, Jul 30 2010, Jul 31 2010
%E A179880 a(36) corrected and more terms added by _Amiram Eldar_, May 24 2025