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Number of divisors of n!! (double factorial = A006882(n)).
2

%I #21 Aug 27 2020 10:09:03

%S 1,1,2,2,4,4,10,8,16,16,36,32,66,64,144,120,192,240,340,480,570,864,

%T 1200,1728,1656,2880,3456,4320,5616,8640,9072,17280,10752,28800,22176,

%U 46080,30240,92160,62208,152064,84240,304128,128000,608256,201600

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

%C It appears that a(n+2) = 2*a(n) if n is in A238526. - _Michel Lagneau_, Dec 07 2015

%H Amiram Eldar, <a href="/A114338/b114338.txt">Table of n, a(n) for n = 0..10000</a>

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

%e a(5) = 4 since 5!! = 15 and the divisors are 1, 3, 5 and 15.

%e 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

%p f := proc(n)

%p numtheory[tau](doublefactorial(n)) ;

%p end proc: # _R. J. Mathar_, Dec 14 2015

%t DivisorSigma[0,Range[50]!! ]

%o (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

%o vector(100, n, n--; numdiv(df(n))) \\ _Altug Alkan_, Dec 07 2015

%Y Cf. A000005, A006882, A027423, A238526.

%K easy,nonn

%O 0,3

%A _Giovanni Resta_, Feb 07 2006