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%I #9 May 03 2021 21:42:55
%S 0,0,0,1,0,3,0,3,1,3,0,10,0,3,3,6,0,10,0,10,3,3,0,21,1,3,3,10,0,21,0,
%T 10,3,3,3,28,0,3,3,21,0,21,0,10,10,3,0,36,1,10,3,10,0,21,3,21,3,3,0,
%U 55,0,3,10,15,3,21,0,10,3,21,0,55,0,3,10,10,3,21,0,36,6,3,0,55
%N Number of pairs (d1, d2) of divisors of n such that d1<d2, d1|n, d2|n, 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(n/k) * c(n/i), where c(n) = 1 - ceiling(n) + floor(n).
%e a(12) = 10; The 10 pairs are (1,2), (1,3), (1,4), (1,6), (2,3), (2,4), (2,6), (3,4), (3,6), (4,6).
%t Table[Sum[Sum[(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), 1))); \\ _Michel Marcus_, May 02 2021
%Y Cf. A343824.
%K nonn
%O 1,6
%A _Wesley Ivan Hurt_, May 02 2021
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