A365228 Denominator of Sum_{1<=j<=k<=n, gcd(j,k)=1} 1/(j*k).
1, 2, 1, 3, 4, 20, 10, 210, 168, 504, 105, 1155, 792, 1560, 60060, 180180, 16016, 123760, 510510, 29099070, 21162960, 335920, 3233230, 74364290, 45762640, 187210800, 13385572200, 40156716600, 97349616, 31054527504, 166363540200, 12033629407800, 2831442213600, 1698865328160
Offset: 1
Crossrefs
Cf. A365227 (numerator of this sum).
Programs
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Maple
A365228 := proc(n) local j,k,s; s := 0; for j from 1 to n do for k from j to n do if gcd(j,k) = 1 then s := s + 1/(j*k); end if; end do; end do; denom(s); end proc; seq(A365228(n), n = 1..30); # second Maple program: a:= n-> denom(add(add(`if`(igcd(j, k)=1, 1/j, 0), j=1..k)/k, k=1..n)): seq(a(n), n=1..45); # Alois P. Heinz, Aug 28 2023
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Mathematica
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 *) -
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
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Python
from fractions import Fraction from math import gcd 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