A056583 Solution to a(n)^(n^2/a(n)) = gcd(n^n, Product_{k

1, 1, 0, 1, 12, 1, 16, 27, 20, 1, 12, 1, 28, 15, 16, 1, 18, 1, 20, 21, 44, 1, 24, 25, 52, 27, 28, 1, 30, 1, 32, 33, 68, 35, 36, 1, 76, 39, 40, 1, 42, 1, 44, 45, 92, 1, 48, 49, 50, 51, 52, 1, 54, 55, 56, 57, 116, 1, 60, 1, 124, 63, 64, 65, 66, 1, 68, 69, 70, 1, 72, 1, 148, 75, 76

Offset: 2

Author

Henry Bottomley, Jul 03 2000

Keywords

• nonn

Examples

			For n = 4, there are no integer solutions of a^(16/a) = 4, though there are two real solutions of about 1.099997 and 43.55926.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 2..20000

Crossrefs

Cf. A000312, A002109, A056582, A056584.

Programs

PARI

A056583(n) = if(2==n, 1, if(4==n, 0, if(8==n, 16, if(9==n, 27, if(isprime(n), 1, if(!(n%2) && isprime(n/2), 2*n, n)))))); \\ Antti Karttunen, Jan 22 2025

Formula

a(2) = 1, a(4) = 0, a(8) = 16, a(9) = 27; if p an odd prime: a(p) = 1 and a(2p) = 4p; otherwise if n>1: a(n) = n. Apart from n = 4, a(n) = n^2/A056584(n) = A056582(n)^(1/A056584(n)).