A337943 Total number of divisors, d, of the sum of the squared parts in each partition of n into two parts, where d < n.

0, 2, 1, 5, 2, 10, 4, 14, 8, 14, 7, 29, 9, 26, 13, 33, 12, 47, 16, 39, 24, 43, 19, 76, 20, 49, 34, 72, 24, 78, 28, 82, 43, 67, 31, 128, 32, 83, 51, 98, 37, 140, 40, 122, 59, 98, 44, 189, 55, 103, 70, 133, 50, 185, 51, 178, 85, 133, 58, 217, 60, 143, 107, 190, 58, 235, 67, 187

Offset

1,2

Links

Table of n, a(n) for n=1..68.

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

Cf. A337944.

Sequence in context: A082010 A318972 A341495 * A275213 A113176 A113175

Adjacent sequences: A337940 A337941 A337942 * A337944 A337945 A337946

Keyword

nonn

Author

Wesley Ivan Hurt, Oct 01 2020

Status

approved