A114338 Number of divisors of n!! (double factorial = A006882(n)).

1, 1, 2, 2, 4, 4, 10, 8, 16, 16, 36, 32, 66, 64, 144, 120, 192, 240, 340, 480, 570, 864, 1200, 1728, 1656, 2880, 3456, 4320, 5616, 8640, 9072, 17280, 10752, 28800, 22176, 46080, 30240, 92160, 62208, 152064, 84240, 304128, 128000, 608256, 201600

Offset: 0

Author

Giovanni Resta, Feb 07 2006

Keywords

• easy
• nonn

Comments

It appears that a(n+2) = 2*a(n) if n is in A238526. - Michel Lagneau, Dec 07 2015

Examples

			a(5) = 4 since 5!! = 15 and the divisors are 1, 3, 5 and 15.
a(6) = 10 because 6!! = A006882(6) = 48 has precisely ten distinct divisors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. - _Michel Lagneau_, Dec 07 2016
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000005, A006882, A027423, A238526.

Programs

Maple

f := proc(n)
numtheory[tau](doublefactorial(n)) ;
end proc: # R. J. Mathar, Dec 14 2015

Mathematica

DivisorSigma[0,Range[50]!! ]

PARI

df(n) = if( n<0, 0, my(E); E = exp(x^2 / 2 + x * O(x^n)); n! * polcoeff( 1 + E * x * (1 + intformal(1 / E)), n)); \\ A006882
vector(100, n, n--; numdiv(df(n))) \\ Altug Alkan, Dec 07 2015

Formula

a(n) = sigma_0(n!!) = tau(n!!) = A000005(A006882(n)).