A280634 Number of partitions of 2n into two refactorable parts.

1, 1, 0, 0, 2, 0, 1, 1, 1, 2, 0, 1, 2, 0, 1, 1, 0, 2, 1, 0, 2, 1, 0, 3, 0, 1, 1, 0, 2, 1, 1, 2, 0, 2, 0, 2, 2, 1, 1, 3, 1, 2, 1, 1, 2, 3, 0, 5, 2, 2, 1, 2, 2, 3, 1, 4, 1, 4, 0, 5, 1, 2, 1, 3, 1, 3, 1, 3, 1, 5, 0, 7, 1, 3, 1, 3, 2, 3, 1, 5, 0, 6, 0, 7, 1, 3, 1, 5, 0, 3

Offset: 1

Author

Wesley Ivan Hurt, Jan 06 2017

Keywords

• nonn
• easy

Examples

			a(5) = 2; There are two partitions of 2*5 = 10 into two refactorable parts: (1,9) and (2,8).
		

Links

• Eric Weisstein's World of Mathematics, Refactorable Number
• Index entries for sequences related to partitions

Crossrefs

Cf. A000005, A033950, A172398, A280226.

Programs

Maple

with(numtheory): A280634:=n->add((1-signum((i mod tau(i))))*(1-signum((2*n-i) mod tau(2*n-i))), i=1..n): seq(A280634(n), n=1..150);

Mathematica

Table[Sum[(1 - Sign[Mod[i, DivisorSigma[0, i]]]) (1 - Sign[Mod[#, DivisorSigma[0, #]]] &[2 n - i]), {i, n}], {n, 90}] (* Michael De Vlieger, Jan 07 2017 *)

Formula

a(n) = Sum_{i=1..n} (1-sign(i mod d(i))) * (1-sign((2n-i) mod d(2n-i))) where d(n) is the number of divisors of n.