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%I #11 Jan 29 2017 01:28:21
%S 2,4,16,1296,9681819840000
%N Minimum number k such that n iterations of products of prime factor exponents are required to reduce k to 1.
%H MathOverflow, <a href="http://mathoverflow.net/questions/143743/product-of-exponents-of-prime-factorization">Product of Exponents of Prime Factorization</a>.
%e The term a(5) = 9681819840000, which factors as 2^9*3^6*5^4*7^3*11^2, because 9*6*4*3*2 = 1296 = 2^4*3^4 and 4*4 = 16 = 2^4 and 4 = 2^2 and 2 = 2^1 gives 1 in 5 iterations of products of prime exponents -- and no smaller positive integer has this property (see link).
%t Table[k = 1; While[Length@ NestWhileList[Times @@ (FactorInteger[#][[All, -1]]) &, k, # > 1 &] - 1 != n, k++]; k, {n, 4}] (* _Michael De Vlieger_, Jan 25 2017 *)
%Y Cf. A005361.
%K nonn,hard
%O 1,1
%A _Rick L. Shepherd_, Jan 09 2017
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