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%I #32 Aug 29 2023 14:29:43
%S 1,3,2,7,11,59,33,737,631,1973,439,4967,3595,7283,289433,891067,82391,
%T 647449,2764637,160300109,119168603,1923477,19032303,442903921,
%U 278705461,1155909107,84109239017,255355122859,632225777,203232858383,1110186816983,81194050820693
%N Numerator of Sum_{1<=j<=k<=n, gcd(j,k)=1} 1/(j*k).
%p A365227 := proc(n)
%p local j,k,s; s := 0;
%p for j from 1 to n do
%p for k from j to n do
%p if gcd(j,k) = 1 then s := s + 1/(j*k);
%p end if;
%p end do;
%p end do;
%p numer(s);
%p end proc;
%p seq(A365227(n), n = 1..20);
%p # second Maple program:
%p a:= n-> numer(add(add(`if`(igcd(j, k)=1, 1/j, 0), j=1..k)/k, k=1..n)):
%p seq(a(n), n=1..45); # _Alois P. Heinz_, Aug 28 2023
%o (Python)
%o from math import gcd
%o from fractions import Fraction
%o def A365227(n): return sum(sum(Fraction(1,j) for j in range(1,k+1) if gcd(j,k)==1)/k for k in range(1,n+1)).numerator # _Chai Wah Wu_, Aug 29 2023
%o (PARI) a(n) = numerator(sum(j=1, n, sum(k=j, n, if (gcd(j,k)==1, 1/(j*k))))); \\ _Michel Marcus_, Aug 28 2023
%Y Cf. A365228 (denominator of this sum).
%K nonn,frac
%O 1,2
%A _Franz Vrabec_, Aug 27 2023
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