cp's OEIS Frontend

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

%I A114338 #21 Aug 27 2020 10:09:03
%S A114338 1,1,2,2,4,4,10,8,16,16,36,32,66,64,144,120,192,240,340,480,570,864,
%T A114338 1200,1728,1656,2880,3456,4320,5616,8640,9072,17280,10752,28800,22176,
%U A114338 46080,30240,92160,62208,152064,84240,304128,128000,608256,201600
%N A114338 Number of divisors of n!! (double factorial = A006882(n)).
%C A114338 It appears that a(n+2) = 2*a(n) if n is in A238526. - _Michel Lagneau_, Dec 07 2015
%H A114338 Amiram Eldar, <a href="/A114338/b114338.txt">Table of n, a(n) for n = 0..10000</a>
%F A114338 a(n) = sigma_0(n!!) = tau(n!!) = A000005(A006882(n)).
%e A114338 a(5) = 4 since 5!! = 15 and the divisors are 1, 3, 5 and 15.
%e A114338 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 A114338 f := proc(n)
%p A114338 numtheory[tau](doublefactorial(n)) ;
%p A114338 end proc: # _R. J. Mathar_, Dec 14 2015
%t A114338 DivisorSigma[0,Range[50]!! ]
%o A114338 (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 A114338 vector(100, n, n--; numdiv(df(n))) \\ _Altug Alkan_, Dec 07 2015
%Y A114338 Cf. A000005, A006882, A027423, A238526.
%K A114338 easy,nonn
%O A114338 0,3
%A A114338 _Giovanni Resta_, Feb 07 2006