A337531 Number of ways that the divisors of 2n can be written as unordered sums of two other prime divisors of 2n (not necessarily distinct).

0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 1, 2, 2, 3, 2, 1, 2, 2, 2, 1, 3, 1, 2, 3, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 5, 1, 2, 3, 1, 2, 3, 1, 2, 2, 4, 1, 2, 1, 2, 3, 2, 2, 3, 1, 2, 1, 2, 1, 3, 2, 2, 2, 2, 1, 4, 2, 2, 2, 2, 2, 2

Offset

1,6

Links

Table of n, a(n) for n=1..96.

Formula

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

Example

a(15) = 3; The divisors of 2*15 = 30 are {1,2,3,5,6,10,15,30} and since 2 + 3 = 5, 3 + 3 = 6 and 5 + 5 = 10, a(15) = 3.

Crossrefs

Cf. A175393.

Sequence in context: A036475 A330746 A316555 * A316556 A187279 A076820

Adjacent sequences: A337528 A337529 A337530 * A337532 A337533 A337534

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 30 2020

Status

approved