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

1, 3, 2, 7, 11, 59, 33, 737, 631, 1973, 439, 4967, 3595, 7283, 289433, 891067, 82391, 647449, 2764637, 160300109, 119168603, 1923477, 19032303, 442903921, 278705461, 1155909107, 84109239017, 255355122859, 632225777, 203232858383, 1110186816983, 81194050820693

Offset

1,2

Links

Table of n, a(n) for n=1..32.

Maple

A365227 := 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;
   numer(s);
end proc;
seq(A365227(n), n = 1..20);
# second Maple program:
a:= n-> numer(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

Prog

(Python)
from math import gcd
from fractions import Fraction
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
(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

Crossrefs

Cf. A365228 (denominator of this sum).

Sequence in context: A099329 A182871 A143329 * A053440 A329724 A143332

Adjacent sequences: A365224 A365225 A365226 * A365228 A365229 A365230

Keyword

nonn,frac

Author

Franz Vrabec, Aug 27 2023

Status

approved