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Sum of the coordinates of all pairs of divisors of n, (d1,d2), such that d1 < d2.
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%I #13 May 21 2021 12:57:05

%S 0,3,4,14,6,36,8,45,26,54,12,140,14,72,72,124,18,195,20,210,96,108,24,

%T 420,62,126,120,280,30,504,32,315,144,162,144,728,38,180,168,630,42,

%U 672,44,420,390,216,48,1116,114,465,216,490,54,840,216,840,240,270,60,1848,62,288

%N Sum of the coordinates of all pairs of divisors of n, (d1,d2), such that d1 < d2.

%C If n = p where p is prime, the only pair of divisors of p such that d1 < d2 is (1,p), whose coordinate sum is a(p) = p + 1. - _Wesley Ivan Hurt_, May 21 2021

%F a(n) = Sum_{d1|n, d2|n, d1<d2} (d1+d2).

%e a(3) = 4; The divisors of 3 are {1,3}. If we form all ordered pairs (d1,d2) such that d1 < d2, we have: (1,3). The sum of the coordinates gives 1+3 = 4.

%e a(4) = 14; The divisors of 4 are {1,2,4}. If we form all ordered pairs (d1,d2) such that d1<d2, we have: (1,2), (1,4), (2,4). The sum of all the coordinates gives 1+2+1+4+2+4 = 14.

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

%o (PARI) a(n) = my(d = divisors(n)); sum(i=1, #d, sum(j=1, i-1, d[i]+d[j])); \\ _Michel Marcus_, Aug 22 2020

%Y Cf. A066446, A184389, A337246.

%K nonn,easy

%O 1,2

%A _Wesley Ivan Hurt_, Aug 21 2020