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A114338 Number of divisors of n!! (double factorial = A006882(n)). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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

MAPLE

f := proc(n)

numtheory[tau](doublefactorial(n)) ;

end proc: # R. J. Mathar, Dec 14 2015

MATHEMATICA

DivisorSigma[0, Range[50]!! ]

PROG

(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

CROSSREFS

Cf. A000005, A006882, A027423, A238526.

Sequence in context: A243330 A318838 A231523 * A170831 A133406 A240381

Adjacent sequences:  A114335 A114336 A114337 * A114339 A114340 A114341

KEYWORD

easy,nonn

AUTHOR

Giovanni Resta, Feb 07 2006

STATUS

approved

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Last modified December 3 14:22 EST 2020. Contains 338906 sequences. (Running on oeis4.)