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A179873 Corresponding values of antiharmonic means B(h) to numbers h from A179871 (numbers h such that antiharmonic mean of the numbers k < h such that gcd(k, h) = 1 is an integer).

%I A179873 #21 May 25 2025 01:47:44
%S A179873 1,1,3,7,7,11,15,15,19,23,27,31,31,35,37,39,39,47,55,55,57,59,61,63,
%T A179873 67,71,71,73,75,77,79,87,89,91,95,97,99,111,111,113,115,119,119,121,
%U A179873 125,127,131,135,137,143,145,151,151,153,155,157,159,165,167,169,171
%N A179873 Corresponding values of antiharmonic means B(h) to numbers h from A179871 (numbers h such that antiharmonic mean of the numbers k < h such that gcd(k, h) = 1 is an integer).
%C A179873 Conjecture: nondecreasing sequence of odd numbers.
%H A179873 Amiram Eldar, <a href="/A179873/b179873.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..2500 from Ivan Neretin)
%F A179873 a(n) = A053818(A179871(n)) / A023896(A179871(n)) = A175505(A179871(n)).
%e A179873 a(6) = A175505(A179871(6)) = A175505(17) = 11 = B(17).
%t A179873 B[n_] := Plus @@ ((ks = Select[Range[n], GCD[n, #] == 1 &])^2)/Plus @@ ks; Select[B /@ Range[215], IntegerQ] (* _Ivan Neretin_, May 22 2015 *)
%o A179873 (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 A179873 list(lim) = {my(m); for(k = 1, lim, m = ah(k); if(denominator(m) == 1, print1(m, ", ")));} \\ _Amiram Eldar_, May 25 2025
%Y A179873 Cf. A179871, A179872, A179874, A179875, A179876, A179877, A179878, A179879, A179880, A179882, A179883, A179884, A179885, A179886, A179887, A179890, A179891.
%K A179873 nonn
%O A179873 1,3
%A A179873 _Jaroslav Krizek_, Jul 30 2010, Jul 31 2010