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%I #22 Dec 07 2023 01:45:57
%S 1,1,5,5,3,13,13,21,53,7,7,49,25,29,31,85,11,109,37,27,43,15,15,193,
%T 83,53,485,113,19,59,61,341,67,23,71,433,73,77,79,107,27,83,85,59,271,
%U 31,31,769,685,167,103,209,35,973,37,449,115,39,39,239,121,125,379,1365
%N Numerator of A053818(n)/A023896(n) = antiharmonic mean of numbers k such that gcd(k,n) = 1, 1 <= k < n.
%C See A175506 - denominators of the antiharmonic means B of numbers k such that gcd(k, n) = 1 for numbers n >= 1 and k < n where B = A053818(n) / A023896(n) = a(n) / A175506(n).
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Contraharmonic_mean">Contraharmonic mean</a>.
%F a(n) = A053818(n) * A175506(n) / A023896(n).
%F Sum_{k=1..n} a(k)/175506(k) ~ n^2/3. - _Amiram Eldar_, Dec 07 2023
%p antiHMean := proc(L)
%p add(i^2,i=L)/add(i,i=L) ;
%p end proc:
%p A175505 := proc(n)
%p local kset,k ;
%p kset := [1] ;
%p for k from 2 to n do
%p if igcd(k,n) = 1 then
%p kset := [op(kset),k] ;
%p end if;
%p end do:
%p antiHMean(kset) ;
%p numer(%) ;
%p end proc: # _R. J. Mathar_, Sep 26 2013
%t f[n_] := 2Plus @@ (Select[ Range@n, GCD[ #, n] == 1 &]^2)/(n*EulerPhi@n); f[1] = 1; Numerator@Array[f, 65] (* _Robert G. Wilson v_, Jul 01 2010 *)
%o (PARI) A175505(n)=numerator(2*n+(-1)^omega(n)*A007947(n)/n)/3) \\ _M. F. Hasler_, Nov 29 2010
%o (PARI) a(n) = {my(f = factor(n)); numerator(if(n == 1, 1, 2*n/3 + (1/3) * prod(i = 1, #f~, 1 - f[i, 1])/eulerphi(f)));} \\ _Amiram Eldar_, Dec 07 2023
%Y Cf. A023896, A053818, A175506 (denominators).
%K nonn,frac
%O 1,3
%A _Jaroslav Krizek_, May 31 2010, Jun 01 2010
%E More terms from _Robert G. Wilson v_, Jul 01 2010
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