A237292 a(n) = A002326(2n(n+1)) / A002326(n).

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 7, 23, 25, 27, 29, 31, 33, 35, 37, 13, 41, 43, 45, 47, 49, 51, 53, 11, 19, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 35, 107, 109, 37, 113, 115, 117, 119, 121, 123, 125

Offset: 0

Author

Thomas Ordowski, Feb 06 2014

Keywords

• nonn

Comments

Note that ((2n+1)^2-1)/2 = 2n(n+1).

We have 1 <= a(n) <= 2n+1 and a(n) divides 2n+1 for every n >= 0.

Odd m is a Wieferich number A182297 if and only if a((m-1)/2) < m.

Odd prime p is a Wieferich prime A001220 if and only if a((p-1)/2) = 1.

a((n-1)/2) = 1 for n = 1, 1093, 3511, 7651, 10533, 14209, 17555, ...

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001220, A002326, A077816 and A182297.

Programs

Maple

1,seq(numtheory:-order(2,4*n*(n+1)+1)/numtheory:-order(2,2*n+1),n=1..100); # Robert Israel, Dec 02 2015

PARI

a002326(n) = znorder(Mod(2, 2*n+1));
a(n) = a002326(2*n*(n+1))/a002326(n); \\ Michel Marcus, Feb 08 2014

Formula

a(n) = ord_{(2n+1)^2}(2) / ord_{2n+1}(2), n >= 0.

Extensions

More terms from Michel Marcus, Feb 08 2014

Edited by Thomas Ordowski, Dec 02 2015