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

1, 2, 12, 720, 907200, 251475840000, 14272938808128000000, 1683176415906545239680000000000, 216212806227686567939021962996416000000000000

Offset: 0

Author

Labos Elemer, May 30 2001

Keywords

• nice
• nonn
• changed

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

Examples

			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.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..23

Crossrefs

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

Programs

Mathematica

a[n_] := Times @@ (Prime[Range[n]]^(Prime[Range[n, 1, -1]]-1)); Array[a, 9, 0] (* Jean-François Alcover, Dec 11 2016, after T. D. Noe *)

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).

a(n) = A005179(A002110(n)). - Amiram Eldar, Aug 26 2025

Extensions

a(0) prepended by Amiram Eldar, Aug 26 2025