A213595 A048784(n) / 2^A213594(n).

1, 1, 3, 1, 9, 3, 1, 3, 3, 3, 1, 3, 3, 3, 15, 3, 3, 9, 3, 9, 1, 1, 15, 27, 9, 3, 15, 1, 5, 5, 3, 9, 9, 9, 3, 3, 1, 3, 45, 9, 15, 1, 15, 15, 15, 45, 9, 81, 9, 5, 5, 1, 25, 5, 3, 3, 5, 5, 3, 15, 27, 9, 21, 3, 81, 9, 3, 15, 1, 3, 75, 81, 9, 9, 135, 27, 25, 15

Offset

1,3

Comments

a(n) = tau(binomial(2*n,n)) / 2^k, where tau = number of divisors (A000005) and k is the greatest possible integer.

Links

Table of n, a(n) for n=1..78.

Example

a(7) = 1 because A048784(7) / 2^5 = 32 / 32 = 1 is integer.

Maple

with(numtheory): for n from 1 to 100 do:ii:=0:for k from 500 by -1 to 1 while(ii=0) do: x:=evalf(tau(binomial(2*n, n))/2^k):if x=floor(x) then ii:=1: printf(`%d, `, floor(x)):else fi:od:od:

Crossrefs

Cf. A048784, A213594.

Sequence in context: A223140 A021762 A019736 * A140303 A249266 A309057

Adjacent sequences: A213592 A213593 A213594 * A213596 A213597 A213598

Keyword

nonn

Author

Michel Lagneau, Jun 15 2012

Status

approved