A337530 Number of ways that the divisors of 2n can be written as the sum of the squares of two other divisors of 2n (not necessarily distinct).

1, 1, 1, 2, 2, 1, 1, 2, 2, 3, 1, 2, 1, 1, 3, 3, 1, 2, 1, 4, 1, 1, 1, 2, 3, 1, 2, 2, 1, 4, 1, 3, 1, 2, 2, 4, 1, 1, 2, 5, 1, 1, 1, 2, 6, 1, 1, 3, 2, 4, 1, 2, 1, 2, 2, 2, 1, 1, 1, 6, 1, 1, 2, 4, 3, 1, 1, 4, 1, 3, 1, 4, 1, 1, 4, 2, 1, 3, 1, 6, 3, 1, 1, 2, 2, 1, 1, 2, 1, 8, 1, 2, 1, 1, 2

Offset

1,4

Comments

a(n) >= 1 since 2n always has 1 and 2 as divisors with 1^2 + 1^2 = 2.

Links

Table of n, a(n) for n=1..95.

Formula

a(n) = Sum_{d1|(2*n), d2|(2*n), d3|(2*n), d1<=d2<=d3} [d1^2 + d2^2 = d3], where [ ] is the Iverson bracket.

Example

a(10) = 3; The divisors of 2*10 = 20 are {1,2,4,5,10,20}. Since 1^2 + 1^2 = 2, 1^2 + 2^2 = 5 and 2^2 + 4^2 = 20, there are 3 total ways.

Crossrefs

Sequence in context: A151552 A160418 A168115 * A269982 A329462 A153864

Adjacent sequences: A337527 A337528 A337529 * A337531 A337532 A337533

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Aug 30 2020

Status

approved