A056676 Number of non-unitary but squarefree divisors of binomial(n,floor(n/2)). Also number of nonsquarefree but unitary divisors of binomial(n,floor(n/2)).

0, 0, 0, 0, 0, 2, 0, 0, 4, 6, 0, 8, 8, 8, 8, 16, 0, 16, 0, 16, 32, 32, 0, 32, 48, 48, 56, 56, 96, 96, 64, 128, 128, 192, 256, 384, 384, 384, 512, 768, 512, 512, 512, 512, 448, 448, 768, 896, 896, 896, 896, 896, 768, 768, 2048, 2048, 4096, 4096, 2048, 2048, 2048, 2048

Offset

1,6

Links

Table of n, a(n) for n=1..62.

Formula

a(n) = A039593(n) - A000005(A055231(x)) = A039593(n) - A000005(A007913(x)/A055229(x)), where x = A001405(n) = binomial(n, floor(n/2)).

a(n) = A039593(n) - A056673(n). - Sean A. Irvine, May 02 2022

Example

n=14, C(14,7)=3432, has 32 divisors, 16 unitary, 16 squarefree. The size of overlap is 8. The complementary parts are: non-unitary/squarefree set={2,6,22,26,66,78,286,828}, while the unitary/not squarefree set of equal size is {8,24,88,104,264,312,1144,3432}. So a(14)=8.

Crossrefs

Cf. A039593, A000005, A055231, A007913, A055229, A001405, A056673.

Sequence in context: A284611 A282551 A333706 * A352450 A098699 A021837

Adjacent sequences: A056673 A056674 A056675 * A056677 A056678 A056679

Keyword

nonn

Author

Labos Elemer, Aug 10 2000

Status

approved