A309397 - OEIS

A309397

a(n) = gcd(n^2, A001008(n-1)) for n > 1.

1, 3, 1, 25, 1, 49, 1, 1, 1, 121, 1, 169, 1, 1, 1, 289, 1, 361, 1, 1, 1, 529, 1, 5, 1, 1, 1, 841, 1, 961, 1, 1, 1, 1, 1, 1369, 1, 1, 1, 1681, 1, 1849, 1, 1, 1, 2209, 1, 7, 1, 1, 1, 2809, 1, 1, 1, 1, 1, 3481, 1, 3721, 1, 1, 1, 1, 1, 4489, 1, 1, 1, 5041, 1, 5329

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OFFSET

2,2

COMMENTS

By Wolstenholme's theorem, if p > 3 is prime, then a(p) = p^2.

Conjecture: for n > 3, if a(n) = n^2, then n is a prime.

Note: the weak pseudoprimes n such that a(n) = n are not known.

Composite numbers m <> p^2 for which a(m) > 1 are the same as in A309391: 88, 1290, 9339, ...

LINKS

Table of n, a(n) for n=2..73.

R. Meštrović, Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862--2012), arXiv:1111.3057 [math.NT], 2011.

Eric Weisstein's World of Mathematics, Wolstenholme's Theorem.