A056584 Solution to (n^2/a(n))^a(n) = gcd(n^n, Product_{k<n} k^k) where a(n) and n^2/a(n) are integers, or 0 if no such integers exist.

4, 9, 0, 25, 3, 49, 4, 3, 5, 121, 12, 169, 7, 15, 16, 289, 18, 361, 20, 21, 11, 529, 24, 25, 13, 27, 28, 841, 30, 961, 32, 33, 17, 35, 36, 1369, 19, 39, 40, 1681, 42, 1849, 44, 45, 23, 2209, 48, 49, 50, 51, 52, 2809, 54, 55, 56, 57, 29, 3481, 60, 3721, 31, 63, 64, 65

Offset

2,1

Links

Table of n, a(n) for n=2..65.

Formula

a(2) = 4, a(4) = 0, a(8) = 4, a(9) = 3; if p an odd prime: a(p) = p^2 and a(2p) = p; otherwise if n>1: a(n) = n. Apart from n = 4, a(n) = n^2/A056583(n) = log(A056582(n))/log(A056583(n)).

Example

For n = 4, there are no integer solutions of (16/a)^a = 4, though there are two real solutions of about 14.5454938 and 0.3673156945.

Crossrefs

Cf. A000312, A002109, A056582, A056583.

Sequence in context: A070439 A298744 A272102 * A135245 A135244 A334657

Adjacent sequences: A056581 A056582 A056583 * A056585 A056586 A056587

Keyword

nonn

Author

Henry Bottomley, Jul 03 2000

Status

approved