%I #8 May 03 2021 21:43:37

%S 0,0,0,1,0,2,0,3,1,2,0,7,0,2,2,6,0,7,0,7,2,2,0,15,1,2,3,7,0,12,0,10,2,

%T 2,2,19,0,2,2,15,0,12,0,7,7,2,0,26,1,7,2,7,0,15,2,15,2,2,0,31,0,2,7,

%U 15,2,12,0,7,2,12,0,37,0,2,7,7,2,12,0,26,6,2,0,31,2,2,2,15

%N Number of pairs (d1, d2) of divisors of n such that d1<d2, d1|n, d2|n, d1|d2 and d1 + d2 <= n.

%C a(n) = 0 if and only if n is noncomposite.

%F a(n) = Sum_{k=1..floor(n/2)} Sum_{i=1..k-1} c(k/i) * c(n/k) * c(n/i), where c(n) = 1 - ceiling(n) + floor(n).

%e a(12) = 7; The 7 pairs are (1,2), (1,3), (1,4), (1,6), (2,4), (2,6), (3,6).

%t Table[Sum[Sum[(1 - Ceiling[k/i] + Floor[k/i]) (1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k - 1}], {k, Floor[n/2]}], {n, 100}]

%o (PARI) a(n) = sumdiv(n, d1, sumdiv(n, d2, if ((d1 < d2) && (d1+d2 <= n) && !(d2 % d1), 1))); \\ _Michel Marcus_, May 02 2021

%Y Cf. A343877.

%K nonn

%O 1,6

%A _Wesley Ivan Hurt_, May 02 2021