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Smallest number with n distinct positive cubic exponents in its prime factorization.
5

%I #5 Aug 10 2021 09:14:52

%S 1,2,768,4403012567040,384637545508886260255243527782400000000

%N Smallest number with n distinct positive cubic exponents in its prime factorization.

%F a(n) = Product_{k=1..n} prime(k)^((n-k+1)^3).

%e a(2)=768, which has a prime factorization of 2^8 * 3^1.

%t Table[Product[Prime[k]^((n - k + 1)^3), {k, 1, n}], {n, 0, 5}] (* _Vaclav Kotesovec_, Aug 10 2021 *)

%Y Subsequence of A025487.

%K nonn

%O 0,2

%A _Matthew Vandermast_, Nov 09 2009