A290109 a(1) = 1; for n > 1, a(n) = x1^(x2^(x3^(x4^...))) where x1, x2, ... are the exponents of the primes present (listed from the smallest prime to the largest) in the prime factorization of n.

1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 3, 2, 1, 1, 1, 5, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 1, 2, 1, 1, 1, 9, 1, 1, 1, 2, 1, 1, 1, 4, 4, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 2, 4, 1, 1, 1, 3, 1, 1, 1, 8, 1, 1, 1, 4, 1, 1, 1, 2, 2, 1, 1, 3

Offset: 1

Author

Antti Karttunen, Aug 27 2017

Keywords

• nonn

Examples

			For n = 300 = 2^2 * 3^1 * 5^2 we have a(300) = 2^(1^2) = 2.
For n = 600 = 2^3 * 3^1 * 5^2 we have a(600) = 3^(1^2) = 3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A028234, A067029.

After a(1) = 1 differs from A087179 for the next time at n=300.

Programs

Scheme

(define (A290109 n) (if (= 1 n) 1 (expt (A067029 n) (A290109 (A028234 n))))) ;; Antti Karttunen, Aug 27 2017

Formula

a(1) = 1; for n > 1, a(n) = A067029(n) ^ a(A028234(n)).