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A237292
a(n) = A002326(2n(n+1)) / A002326(n).
2
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
0,2
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
FORMULA
a(n) = ord_{(2n+1)^2}(2) / ord_{2n+1}(2), n >= 0.
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
PROG
(PARI) a002326(n) = znorder(Mod(2, 2*n+1));
a(n) = a002326(2*n*(n+1))/a002326(n); \\ Michel Marcus, Feb 08 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Ordowski, Feb 06 2014
EXTENSIONS
More terms from Michel Marcus, Feb 08 2014
Edited by Thomas Ordowski, Dec 02 2015
STATUS
approved