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a(n) = Product_{d | n} tau(d).
12

%I #45 Aug 05 2020 21:18:40

%S 1,2,2,6,2,16,2,24,6,16,2,288,2,16,16,120,2,288,2,288,16,16,2,9216,6,

%T 16,24,288,2,4096,2,720,16,16,16,46656,2,16,16,9216,2,4096,2,288,288,

%U 16,2,460800,6,288,16,288,2,9216,16,9216,16,16,2,5308416,2

%N a(n) = Product_{d | n} tau(d).

%H Antti Karttunen, <a href="/A211776/b211776.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = Product_{i=1..omega(n)} (b_i+1)!^(tau(n)/(b_i+1)), where omega(n) is the number of distinct prime factors of n, tau(n) is the number of divisors of n, and n = p_1^(b_1)*p_2^(b_2)* ... *p_{omega(n)}^(b_{omega(n)}). - _Anand Rao Tadipatri_, Aug 04 2020

%e For n = 6: divisors of 6: 1, 2, 3, 6; tau(d): 1, 2, 2, 4; product _{d | n} tau(d) = 1*2*2*4 = 16, where tau = A000005.

%p A211776 := proc(n)

%p mul( A000005(d),d=numtheory[divisors](n)) ;

%p end proc:

%p seq(A211776(n),n=1..20) ; # _R. J. Mathar_, Feb 13 2019

%t Table[Product[DivisorSigma[0, i], {i, Divisors[n]}], {n, 100}] (* _T. D. Noe_, Apr 26 2012 *)

%t a[1] = 1; a[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, d = Times @@ (e + 1); Times @@ ((e + 1)!^(d/(e + 1)))]; Array[a, 100] (* using the Formula section, _Amiram Eldar_, Aug 04 2020 *)

%o (PARI)

%o A211776(n) = { my(m=1); fordiv(n, d, m *= numdiv(d)); m };

%o A211776(n) = prod(d=1, n, if((n % d), 1, numdiv(d)));

%o \\ _Antti Karttunen_, May 19 2017

%Y Cf. A000005, A001221, A007425 (Sum_{d | n} tau(d)).

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Apr 20 2012