A212170 a(n) = first counting number with n distinct positive square exponents in its prime factorization.

1, 2, 48, 207360, 5643509760000, 74508333765820416000000000, 68238227014337640914957453230080000000000000000, 958098594568198616022876832154309463351366075411333120000000000000000000000000

Offset: 1

Author

Matthew Vandermast, May 24 2012

Keywords

• nonn

Comments

Next term has 122 digits.

A166469(a(n))=(n+1)! Cf. A000142.

Examples

			a(2) = 48 = 2^4*3^1 has 2 distinct positive square exponents in its prime factorization (4 and 1 are both perfect squares).  48 is the smallest number with this property.
Also, 48 has 3! = 6 divisors that are not divisible by any pair of consecutive primes: 1, 2, 3, 4, 8 and 16. Cf. A166469.
		

Links

• Dario Alpern, Factorization using the Elliptic Curve Method

Crossrefs

Cf. A000290.

Subsequence of A025487. Also see A002110, A006939, A066120, A166475, A167448.