A070956 Number of pairs (x,y) such that n = gcd(x,y) + lcm(x,y).

0, 1, 1, 2, 1, 3, 2, 3, 2, 3, 2, 5, 2, 4, 4, 5, 1, 5, 2, 5, 5, 5, 2, 7, 3, 4, 4, 6, 2, 8, 4, 6, 4, 4, 5, 9, 2, 4, 5, 8, 2, 9, 4, 7, 7, 5, 2, 10, 4, 6, 4, 7, 2, 8, 5, 9, 5, 5, 2, 12, 4, 6, 8, 8, 4, 10, 4, 6, 5, 10, 4, 12, 2, 4, 8, 7, 6, 10, 4, 11, 6, 4, 2, 13, 6, 7, 5, 10, 2, 13, 8, 8, 7, 5, 5, 13, 2, 7, 7

Offset

1,4

Comments

a(n)=1 for n prime = 2,3,5,17,257,...;

a(n)=2 if n = 4 or 9, or n is in A067466(k).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

a[n_] := Sum[Sum[If[(g = GCD[i, j]) + i*j/g == n, 1, 0], {j, 1, i}], {i, 1, n}]; Array[a, 100] (* Amiram Eldar, Jun 06 2022 *)

Prog

(PARI) a(n) = sum(i=1, n, sum(j=1, i, n == gcd(i, j)+lcm(i, j))); \\ Michel Marcus, Feb 16 2021

Crossrefs

Cf. A067466.

Sequence in context: A305030 A110917 A329340 * A237127 A262746 A007828

Adjacent sequences: A070953 A070954 A070955 * A070957 A070958 A070959

Keyword

easy,nonn

Author

Benoit Cloitre, May 16 2002

Status

approved