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A179878 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 an integer (see A179882).

%I A179878 #21 May 28 2025 10:52:30
%S A179878 2,11,23,47,59,83,107,167,179,227,263,266,347,359,383,455,467,470,479,
%T A179878 494,503,506,518,563,587,590,719,782,839,863,887,890,902,911,935,983,
%U A179878 986,1019,1166,1178,1187,1235,1283,1295,1307,1319,1334,1358,1367,1394
%N A179878 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 an integer (see A179882).
%C A179878 For corresponding values of numbers h-1 see A179877. Subsequence of A179876, A179871 and A179883.
%H A179878 Amiram Eldar, <a href="/A179878/b179878.txt">Table of n, a(n) for n = 1..10000</a>
%F A179878 a(n) = A179877(n) + 1. - _Amiram Eldar_, May 24 2025
%t A179878 With[{s = Partition[Table[Mean[#^2]/Mean[#] &@ Select[Range[n - 1], GCD[#, n] == 1 &], {n, 1400}], 2, 1]}, 1 + Position[s, _?(And[IntegerQ@ First@ #, SameQ @@ #] &), 1, Heads -> False][[All, 1]]] (* _Michael De Vlieger_, Jul 30 2018 *)
%o A179878 (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 A179878 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 A179878 Cf. A179871, A179872, A179873, A179874, A179875, A179876, A179877, A179879, A179880, A179882, A179883, A179884, A179885, A179886, A179887, A179890, A179891.
%K A179878 nonn
%O A179878 1,1
%A A179878 _Jaroslav Krizek_, Jul 30 2010, Jul 31 2010