Observations on A071553

David Wilson davidwwilson at attbi.com
Tue Jun 11 21:11:37 CEST 2002

Regarding A071553:

Let a(n) = A071553(n), m(n) = A003418(n) = lcm(1,2,...,n).

We then have

a(n) = least x > 1 such that x^n == 1 (mod m(n)).

Observing that (m(n)+1)^n == 1 (mod m(n)), we see that
m(n)+1 is an upper bound for a(n).

I also highly suspect that a(n)-1 always divides m(n).  In this case,
computation of a(n) is much easier, since we only have to consider
possible a(n) of the form (divisor of m(n))+1.

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