

A212170


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


3



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

1,2


COMMENTS

Next term has 122 digits.
A166469(a(n))=(n+1)! Cf. A000142.


LINKS

Table of n, a(n) for n=1..8.
D. Alpern, Factorization using the Elliptic Curve Method


EXAMPLE

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.


CROSSREFS

Cf. A000290.
Subsequence of A025487. Also see A002110, A006939, A066120, A166475, A167448.
Sequence in context: A203778 A203305 A191954 * A057527 A166475 A152688
Adjacent sequences: A212167 A212168 A212169 * A212171 A212172 A212173


KEYWORD

nonn


AUTHOR

Matthew Vandermast, May 24 2012


STATUS

approved



