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
Crossrefs
Cf. A365228 (denominator of this sum).
Programs
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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
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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
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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