

A056583


Solution to a(n)^(n^2/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.


2



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
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OFFSET

2,5


LINKS

Table of n, a(n) for n=2..76.


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)).


EXAMPLE

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.


CROSSREFS

Cf. A000312, A002109, A056582, A056584.
Sequence in context: A322762 A070649 A255864 * A281823 A139724 A040155
Adjacent sequences: A056580 A056581 A056582 * A056584 A056585 A056586


KEYWORD

nonn


AUTHOR

Henry Bottomley, Jul 03 2000


STATUS

approved



