A392835 Number of ordered pairs (i,j) with 1<=i,j<=n such that gcd(i+j,i*j) = gcd(i,j).

1, 3, 8, 14, 23, 29, 42, 56, 73, 87, 108, 126, 151, 171, 194, 224, 257, 281, 318, 350, 387, 419, 464, 502, 551, 589, 642, 688, 745, 783, 844, 906, 963, 1013, 1078, 1138, 1211, 1267, 1336, 1406, 1487, 1539, 1624, 1700, 1781, 1849, 1942, 2024, 2121, 2195

Offset

1,2

Links

Table of n, a(n) for n=1..50.

Thang Pang Ern, Malcolm Tan Jun Xi, and Loh Wei Xuan Ryan, On the Limiting Density of a gcd Map, arXiv:2512.22494 [math.NT], 2025.

Mathematica

a[n_]:=Sum[Sum[Boole[GCD[i+j, i*j]==GCD[i, j]], {j, n}], {i, n}]; Array[a, 50] (* Stefano Spezia, Jan 25 2026 *)

Prog

(PARI) a(n) = sum(i=1, n, sum(j=1, n, gcd(i+j, i*j) == gcd(i, j))); \\ Michel Marcus, Jan 24 2026

Crossrefs

Limiting density of a(n)/n^2 is A065465.

Sequence in context: A366087 A022947 A098762 * A014848 A140479 A264689

Adjacent sequences: A392832 A392833 A392834 * A392836 A392837 A392838

Keyword

nonn

Author

Pang Ern, Jan 24 2026

Status

approved