%I #14 Aug 24 2020 22:46:45
%S 0,2,3,14,5,41,7,70,39,87,11,245,13,149,143,310,17,455,19,539,241,321,
%T 23,1165,155,431,390,945,29,1521,31,1302,509,699,467,2639,37,857,679,
%U 2595,41,2687,43,2093,1664,1221,47,5053,399,2387,1091,2835,53,4370,951,4585,1333,1887,59
%N Sum of the products of all pairs of divisors of n, (d1,d2), such that d1|n, d2|n, d1|d2 and d1<d2.
%C Total area of all distinct nonsquare rectangles that can be made whose side lengths are divisors of n and whose length is an integer multiple of its width.
%F a(n) = Sum_{d1|n, d2|n, d1|d2, d1<d2} d1*d2.
%F a(n) = n if and only if n is prime. - _Bernard Schott_, Aug 24 2020
%t Table[Sum[Sum[(i*k) (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, n}], {n, 80}]
%Y Cf. A001001, A119616.
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, Aug 23 2020
|