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A056061 Number of square divisors of central binomial coefficients. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

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

FORMULA

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

EXAMPLE

n=27: binomial(27,1) = 20058300, its largest square-divisor is 900=30^2 so a(27) = tau(30) = 8.

MATHEMATICA

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

PROG

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

CROSSREFS

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

Sequence in context: A166288 A249138 A056648 * A029265 A103648 A127309

Adjacent sequences:  A056058 A056059 A056060 * A056062 A056063 A056064

KEYWORD

nonn

AUTHOR

Labos Elemer Jul 26 2000

STATUS

approved

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Last modified June 26 19:45 EDT 2017. Contains 288766 sequences.