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A280634 Number of partitions of 2n into two refactorable parts. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A053692 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

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Last modified February 19 13:03 EST 2020. Contains 332044 sequences. (Running on oeis4.)