cp's OEIS Frontend

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

%I A070956 #16 Jun 06 2022 05:47:26
%S A070956 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,
%T A070956 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,
%U A070956 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
%N A070956 Number of pairs (x,y) such that n = gcd(x,y) + lcm(x,y).
%C A070956 a(n)=1 for n prime = 2,3,5,17,257,...;
%C A070956 a(n)=2 if n = 4 or 9, or n is in A067466(k).
%H A070956 Amiram Eldar, <a href="/A070956/b070956.txt">Table of n, a(n) for n = 1..10000</a>
%t A070956 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 *)
%o A070956 (PARI) a(n) = sum(i=1, n, sum(j=1, i, n == gcd(i,j)+lcm(i,j))); \\ _Michel Marcus_, Feb 16 2021
%Y A070956 Cf. A067466.
%K A070956 easy,nonn
%O A070956 1,4
%A A070956 _Benoit Cloitre_, May 16 2002