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

1,4

Links

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

Formula

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

Example

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.

Prog

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

Crossrefs

Cf. A028234, A067029.

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

Sequence in context: A371733 A067029 A087179 * A302045 A302035 A307907

Adjacent sequences: A290106 A290107 A290108 * A290110 A290111 A290112

Keyword

nonn

Author

Antti Karttunen, Aug 27 2017

Status

approved