[seqfan] Conjecture: a(n) = n only if n = 1 or 9

Alonso Del Arte alonso.delarte at gmail.com
Thu Apr 15 22:56:06 CEST 2021

Given a(n) = a(n) = \prod_{i = 1}^{n - 1} gcd(i, n) (A051190) it is obvious
that a(n) = 1 only if n is 1 or a prime.

For many OEIS entries Charles has given a heuristic for growth, though not
for this one. It seems to be a decent fraction of n! for composite n.

Of course this doesn't rule out that there might be some larger n such that
a(n) = n.

Thoughts, anyone?


Alonso del Arte
Author at SmashWords.com
Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>

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