A056584 Solution to (n^2/a(n))^a(n) = gcd(n^n, Product_{k

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

Author

Henry Bottomley, Jul 03 2000

Keywords

• nonn

Examples

			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.

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)).