A068795 In prime factorization of n replace all primes with the greatest prime factor of n; a(1)=1.

1, 2, 3, 4, 5, 9, 7, 8, 9, 25, 11, 27, 13, 49, 25, 16, 17, 27, 19, 125, 49, 121, 23, 81, 25, 169, 27, 343, 29, 125, 31, 32, 121, 289, 49, 81, 37, 361, 169, 625, 41, 343, 43, 1331, 125, 529, 47, 243, 49, 125, 289, 2197, 53, 81, 121, 2401, 361, 841, 59, 625, 61

Offset: 1

Author

Reinhard Zumkeller, Mar 05 2002

Keywords

• nonn

Examples

			a(30) = a(2*3*5) = 5*5*5 = 125.
		

Crossrefs

Cf. A001222, A006530, A068794.

Programs

Maple

with(NumberTheory): A068795 := n -> max(PrimeFactors(n))^Omega(n):
seq(A068795(n), n = 1..61);  # Peter Luschny, Oct 25 2024

Formula

a(n) = A006530(n)^A001222(n).

A068794(n) <= n <= a(n).

a(n) = A068794(n) iff n = 1 or n = p^k for some prime p, k > 0.