A181555 a(n) = A002110(n)^n.

1, 2, 36, 27000, 1944810000, 65774855015100000, 733384949590939374729000000, 9037114296609938214167920266348510000000, 78354300210436852307898467208663359164858967744100000000

Offset: 0

Author

Matthew Vandermast, Oct 31 2010

Keywords

• easy
• nonn

Comments

For n>0, a(n)= first counting number whose prime signature consists of n repeated n times (cf. A002024). Subsequence of A025487.

Examples

			a(4) = 1944810000 = 210^4 = 2^4 * 3^4 * 5^4 * 7^4.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..26

Crossrefs

A061742(n) = A002110(n)^2. See also A006939, A066120, A166475, A167448.

A000005(a(n)) = A000169(n). The divisors of a(n) appear as the first A000169(n) terms of A178479, with A178479(A000169(n)) = a(n).

A071207(n, k) gives the number of divisors of n with (n-k) distinct prime factors, A181567(n, k) gives the number of divisors of n with k prime factors counted with multiplicity.

Cf. A001221, A001222, A079474, A146290, A146292.

Programs

Mathematica

a[0] = 1; a[n_] := Product[Prime[i], {i, 1, n}]^n; Array[a, 9, 0] (* Amiram Eldar, Aug 08 2019 *)

Formula

a(n) = A079474(2n,n). - Alois P. Heinz, Aug 22 2019