A280890 Minimum number k such that n iterations of products of prime factor exponents are required to reduce k to 1.

2, 4, 16, 1296, 9681819840000

Offset: 1

Author

Rick L. Shepherd, Jan 09 2017

Keywords

• nonn
• hard

Examples

			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).
		

Links

• MathOverflow, Product of Exponents of Prime Factorization.

Crossrefs

Cf. A005361.

Programs

Mathematica

Table[k = 1; While[Length@ NestWhileList[Times @@ (FactorInteger[#][[All, -1]]) &, k, # > 1 &] - 1 != n, k++]; k, {n, 4}] (* Michael De Vlieger, Jan 25 2017 *)