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%I #20 Jul 09 2023 12:20:09
%S 2,12,720,907200,251475840000,14272938808128000000,
%T 1683176415906545239680000000000,
%U 216212806227686567939021962996416000000000000
%N Smallest number whose number of divisors = n-th primorial (A002110).
%C The n-th term is divisible by the product of first n primorial numbers (A006939(n)), the n-th Chernoff-number. Also the numbers are refactorable (A033950).
%C The formula computes a(n) correctly. - _T. D. Noe_, May 17 2010
%H Michael De Vlieger, <a href="/A061149/b061149.txt">Table of n, a(n) for n = 1..23</a>
%F The n-th term is constructed as a product of special powers of the first n primes, as follows: a(n) = Product_{j=1..n} prime(j)^(prime(n-j+1)-1).
%e a(1)=2, a(2) = (2^2)*(3^1) = 12, a(3) = (2^4)*(3^2)*(5^1) = 720, ..., a(7) = (2^16)*(3^12)*(5^10)*(7^6)*(11^4)*(13^2)*(17^1) = 1683176415906545239680000000000. a(7) is divisible by the product of the first 7 primorial numbers(=A006939(7)): a(7)/2677277333530800000 = 628689600000.
%t a[n_] := Times @@ (Prime[Range[n]]^(Prime[Range[n, 1, -1]]-1)); Array[a, 8] (* _Jean-François Alcover_, Dec 11 2016, after _T. D. Noe_ *)
%Y Cf. A000005, A002110, A005179, A006093, A006939, A025487, A033950.
%K nice,nonn
%O 1,1
%A _Labos Elemer_, May 30 2001
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