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A365228 Denominator of Sum_{1<=j<=k<=n, gcd(j,k)=1} 1/(j*k).

%I A365228 #23 Aug 29 2023 10:12:30
%S A365228 1,2,1,3,4,20,10,210,168,504,105,1155,792,1560,60060,180180,16016,
%T A365228 123760,510510,29099070,21162960,335920,3233230,74364290,45762640,
%U A365228 187210800,13385572200,40156716600,97349616,31054527504,166363540200,12033629407800,2831442213600,1698865328160
%N A365228 Denominator of Sum_{1<=j<=k<=n, gcd(j,k)=1} 1/(j*k).
%p A365228 A365228 := proc(n)
%p A365228    local j,k,s; s := 0;
%p A365228    for j from 1 to n do
%p A365228       for k from j to n do
%p A365228          if gcd(j,k) = 1 then s := s + 1/(j*k);
%p A365228          end if;
%p A365228       end do;
%p A365228    end do;
%p A365228    denom(s);
%p A365228 end proc;
%p A365228 seq(A365228(n), n = 1..30);
%p A365228 # second Maple program:
%p A365228 a:= n-> denom(add(add(`if`(igcd(j, k)=1, 1/j, 0), j=1..k)/k, k=1..n)):
%p A365228 seq(a(n), n=1..45);  # _Alois P. Heinz_, Aug 28 2023
%t A365228 a[n_Integer]:=Module[{sum,j,k},sum=Sum[If[GCD[j,k]==1,1/(j*k),0],{j,1,n},{k,j,n}]; Denominator[sum]]; Table[a[n],{n,1,34}] (* _Robert P. P. McKone_, Aug 29 2023 *)
%o A365228 (PARI) a(n) = denominator(sum(j=1, n, sum(k=j, n, if (gcd(j,k)==1, 1/(j*k))))); \\ _Michel Marcus_, Aug 28 2023
%o A365228 (Python)
%o A365228 from fractions import Fraction
%o A365228 from math import gcd
%o A365228 def A365228(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)).denominator # _Chai Wah Wu_, Aug 29 2023
%Y A365228 Cf. A365227 (numerator of this sum).
%K A365228 nonn,frac
%O A365228 1,2
%A A365228 _Franz Vrabec_, Aug 28 2023