A087179 a(n) = (...(((x1^x2)^x3)^x4)^...) where x1,x2,... are the exponents in the prime factorization of n, a(1) = 0.

0, 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

Sam Alexander, Oct 19 2003

Keywords

• nonn

Examples

			a(75) = a((3^1)*(5^2)) = 1^2 = 1.
a(108) = a((2^2)*(3^3)) = 2^3 = 8.
a(300) = a(2^2 * 3^1 * 5^2) = (2^1)^2 = 4. - _Antti Karttunen_, Aug 27 2017
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• MathMedics, The Prime Factorization of the First 1000 Integers

Crossrefs

Cf. A001221, A051119, A067029, A071178.

After a(1) = 0 differs from A290109 for the next time at n=300.

Programs

Scheme

(define (A087179 n) (if (<= (A001221 n) 1) (A067029 n) (expt (A087179 (A051119 n)) (A071178 n)))) ;; Antti Karttunen, Aug 27 2017

Formula

If A001221(n) <= 1, a(n) = A067029(n) [i.e., when n is a prime power, p^k, a(n) = k], otherwise a(n) = a(A051119(n)) ^ A071178(n). - Antti Karttunen, Aug 27 2017

Extensions

Term a(1) = 0 prepended by Antti Karttunen, Aug 27 2017