A368684 Number of partitions of n into 2 parts such that the smaller part divides both n and floor(n/2).

0, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 4, 1, 3, 1, 4, 1, 2, 1, 6, 1, 2, 1, 4, 1, 4, 1, 5, 1, 2, 1, 6, 1, 2, 1, 6, 1, 4, 1, 4, 1, 2, 1, 8, 1, 3, 1, 4, 1, 4, 1, 6, 1, 2, 1, 8, 1, 2, 1, 6, 1, 4, 1, 4, 1, 4, 1, 9, 1, 2, 1, 4, 1, 4, 1, 8, 1, 2, 1, 8, 1, 2, 1, 6, 1, 6

Offset

1,4

Comments

Essentially, A000005 interspersed with 1's [prepend 0].

Number of divisors of A057979(n+1) for n >= 2.

Links

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

Index entries for sequences related to partitions

Formula

a(n) = A000005(A057979(n+1)) for n >= 2.

a(2n-1) = A060576(n), a(2n) = A000005(n).

a(n) = d(floor((n+1)/2))^((n+1) mod 2), for n >= 2.

a(n) = d( (n+2+(n-2)*(-1)^n)/4 ) for n >= 2.

a(n) = Sum_{k=1..floor(n/2)} c(n/k) * c(floor(n/2)/k), where c(m) = 1 - ceiling(m) + floor(m).

Mathematica

Join[{0}, Table[DivisorSigma[0, (n+2+(n-2)*(-1)^n)/4], {n, 2, 100}]]

Crossrefs

Bisections: A060576, A000005.

Cf. A057979.

Sequence in context: A066075 A359211 A072347 * A351034 A318831 A303710

Adjacent sequences: A368681 A368682 A368683 * A368685 A368686 A368687

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 03 2024

Status

approved