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%I #11 Jul 08 2023 16:12:11
%S 1,2,48,207360,5643509760000,74508333765820416000000000,
%T 68238227014337640914957453230080000000000000000,
%U 958098594568198616022876832154309463351366075411333120000000000000000000000000
%N a(n) = first counting number with n distinct positive square exponents in its prime factorization.
%C Next term has 122 digits.
%C A166469(a(n))=(n+1)! Cf. A000142.
%H Dario Alpern, <a href="https://www.alpertron.com.ar/ecm.htm">Factorization using the Elliptic Curve Method</a>
%e 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.
%e 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.
%Y Cf. A000290.
%Y Subsequence of A025487. Also see A002110, A006939, A066120, A166475, A167448.
%K nonn
%O 1,2
%A _Matthew Vandermast_, May 24 2012
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