OFFSET
1,2
FORMULA
a(n) = Sum_{i=1..floor(n/2)} Sum_{k=1..n} (1 - ceiling((i^2+(n-i)^2)/k) + floor((i^2+(n-i)^2)/k)).
EXAMPLE
a(4) = 5; 4 has two partitions into two parts (3,1) and (2,2). The sums of the squares of these partitions are 3^2 + 1^2 = 10 and 2^2 + 2^2 = 8. Among the positive integers from 1..4, 1 divides 8 and 10, 2 divides 8 and 10 and 4 divides 8, so a(4) = 5.
MATHEMATICA
Table[Sum[Sum[1 - Ceiling[(i^2 + (n - i)^2)/k] + Floor[(i^2 + (n - i)^2)/k], {k, n}], {i, Floor[n/2]}], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Oct 01 2020
STATUS
approved