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

1,5

Links

Table of n, a(n) for n=1..90.

Eric Weisstein's World of Mathematics, Refactorable Number

Index entries for sequences related to partitions

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.

Example

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

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 *)

Crossrefs

Cf. A000005, A033950, A172398, A280226.

Sequence in context: A341024 A286934 A282714 * A281491 A099494 A030341

Adjacent sequences: A280631 A280632 A280633 * A280635 A280636 A280637

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 06 2017

Status

approved