OFFSET
1,2
COMMENTS
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.
EXAMPLE
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.
MATHEMATICA
Table[(# (# + 1)/2) &[
First[Select[Divisors[n], # >= Sqrt[n] &]]] (# (# + 1)/2) &[
Last[Select[Divisors[n], # <= Sqrt[n] &]]], {n, 80}]
PROG
(PARI) t(n) = n*(n+1)/2; \\ A000217
largdiv(n) = if(n<2, 1, my(d=divisors(n)); d[(length(d)+1)\2]); \\ A033676
a(n) = my(d=largdiv(n)); t(d)*t(n/d); \\ Michel Marcus, Jul 18 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Steven Lu, Jul 04 2022
STATUS
approved