A056061 Number of square divisors of central binomial coefficients.

1, 1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 4, 4, 8, 8, 4, 6, 2, 2, 2, 4, 2, 4, 4, 4, 2, 4, 2, 2, 2, 2, 8, 12, 4, 8, 8, 8, 8, 8, 4, 6, 2, 2, 2, 3, 2, 3, 3, 3, 4, 4, 2, 4, 2, 4, 4, 4, 1, 2, 2, 2, 4, 4, 8, 12, 2, 4, 12, 12, 4, 4, 8, 12, 12, 12, 4, 6, 8, 12, 12, 12, 8, 16, 8, 8, 6

Offset: 1

Author

Labos Elemer Jul 26 2000

Keywords

• nonn

Examples

			n=27: binomial(27,13) = 20058300, its largest square-divisor is 900=30^2 so a(27) = tau(30) = 8.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..120

Crossrefs

Cf. A001405, A046951, A000005, A000188, A056056, A056057, A056058, A056059, A056060.

Programs

Mathematica

Table[Count[Divisors@ Binomial[n, Floor[n/2]], d_ /; IntegerQ@ Sqrt@ d], {n, 0, 84}] (* Michael De Vlieger, Feb 18 2017 *)

PARI

a(n) = sumdiv(binomial(n, n\2), d, issquare(d)); \\ Michel Marcus, Feb 19 2017

Formula

a(n) = A046951(A001405(n)) = A000005(A000188(A001405(n))).