A343824 - OEIS

%I #12 May 01 2021 22:17:05

%S 0,2,2,9,2,24,2,28,12,32,2,96,2,40,36,75,2,126,2,132,44,56,2,288,18,

%T 64,52,168,2,336,2,186,60,80,52,495,2,88,68,400,2,432,2,240,198,104,2,

%U 760,24,258,84,276,2,528,68,512,92,128,2,1296,2,136,246,441,76,624,2,348

%N Sum of the elements in all pairs (d1, d2) of divisors of n such that d1<=d2, d1|n, d2|n, and d1 + d2 <= n.

%C If n is prime, then a(n) = 2.

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

%e a(7) = 2; There is one divisor pair of 7 whose sum is less than or equal to 7: (1,1). The sum is then 1+1 = 2.

%e a(9) = 12; The divisor pairs of 9 whose sum is less than or equal to 9 are: (1,1), (1,3) and (3,3). The sum of the coordinates is then (1+1) + (1+3) + (3+3) = 12.

%t Table[Sum[Sum[(i + k) (1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k}], {k, Floor[n/2]}], {n, 80}]

%o (PARI) a(n) = sumdiv(n, d1, sumdiv(n, d2, if ((d1 <= d2) && (d1+d2 <= n), d1+d2))); \\ _Michel Marcus_, May 01 2021

%Y Cf. A066446.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Apr 30 2021