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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).
0
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.
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Aug 30 2020
STATUS
approved