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

1,2

Links

Table of n, a(n) for n=1..34.

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A365227 (numerator of this sum).

Sequence in context: A141487 A217103 A099866 * A370550 A276811 A317750

Adjacent sequences: A365225 A365226 A365227 * A365229 A365230 A365231

Keyword

nonn,frac

Author

Franz Vrabec, Aug 28 2023

Status

approved