A061149 Smallest number whose number of divisors = n-th primorial (A002110).

2, 12, 720, 907200, 251475840000, 14272938808128000000, 1683176415906545239680000000000, 216212806227686567939021962996416000000000000

Offset

1,1

Comments

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).

The formula computes a(n) correctly. - T. D. Noe, May 17 2010

Links

Michael De Vlieger, Table of n, a(n) for n = 1..23

Formula

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).

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A000005, A002110, A005179, A006093, A006939, A025487, A033950.

Sequence in context: A230265 A060055 A363234 * A191555 A222207 A129933

Adjacent sequences: A061146 A061147 A061148 * A061150 A061151 A061152

Keyword

nice,nonn

Author

Labos Elemer, May 30 2001

Status

approved