A061234 Smallest number with prime(n)^2 divisors where prime(n) is the n-th prime.

6, 36, 1296, 46656, 60466176, 2176782336, 2821109907456, 101559956668416, 131621703842267136, 6140942214464815497216, 221073919720733357899776, 10314424798490535546171949056, 13367494538843734067838845976576

Offset: 1

Author

Labos Elemer, Jun 01 2001

Keywords

• nonn

Examples

			1296 = 2*2*2*2*3*3*3*3 is the smallest number with 25 divisors.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..208

Crossrefs

Cf. A000005, A000040, A001248, A003680, A005179, A037992, A061148, A061149, A061283, A061286.

Formula

a(n) = Min_{x : d(x) = A000005(x) = p(n)^2} = 6^(p(n)-1) because x = 2^(pp-1) > 2^(p-1)3^(p-1) holds if p > 1.

a(n) = A005179(A001248(n)). - Amiram Eldar, Jun 21 2024