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%I #20 Sep 21 2022 00:36:45
%S 1,3,6,9,15,18,28,30,36,45,66,60,91,84,90,100,153,126,190,150,168,198,
%T 276,210,225,273,270,280,435,315,496,360,396,459,420,441,703,570,546,
%U 540,861,588,946,660,675,828,1128,756,784,825,918,910,1431,945,990,1008,1140,1305,1770
%N a(n) = A000217(A033676(n)) * A000217(A033677(n)).
%C When n squares are arranged in a rectangular grid which is as nearly square as possible, a(n) represents the count of rectangles in the grid. The whole grid itself must be a rectangle too.
%e For n=10, the grid as nearly square as possible is 2*5. Thus a(10)=3*15=45 is the number of rectangles in this grid.
%t Table[(# (# + 1)/2) &[
%t First[Select[Divisors[n], # >= Sqrt[n] &]]] (# (# + 1)/2) &[
%t Last[Select[Divisors[n], # <= Sqrt[n] &]]], {n, 80}]
%o (PARI) t(n) = n*(n+1)/2; \\ A000217
%o largdiv(n) = if(n<2, 1, my(d=divisors(n)); d[(length(d)+1)\2]); \\ A033676
%o a(n) = my(d=largdiv(n)); t(d)*t(n/d); \\ _Michel Marcus_, Jul 18 2022
%Y Cf. A000217, A033676, A033677.
%K nonn
%O 1,2
%A _Steven Lu_, Jul 04 2022
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