cp's OEIS Frontend

A365227 Numerator of Sum_{1<=j<=k<=n, gcd(j,k)=1} 1/(j*k).

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