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%I #15 Sep 08 2022 08:46:15
%S 1,2,2,1,3,2,2,4,1,2,3,1,5,18,2,1,5,12,2,12,1,2,6,1,7,8,2,20,9,2,2,6,
%T 3,2,11,1,1,20,15,1,27,2,4,28,1,4,5,36,1,30,2,1,3,2,2,36,1,44,6,24,11,
%U 20,50,1,7,2,3,36,1,2,23,60,7,42,2,1,6,20,2
%N Multiplicative order of 2^n mod 2*n+1.
%H Robert Israel, <a href="/A266697/b266697.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicativeOrder.html">Multiplicative Order</a>
%F a(n) = A002326(n)/gcd(n,A002326(n)). - _Robert Israel_, Jan 10 2016
%p 1,seq(numtheory:-order(2^n,2*n+1),n=1..100); # _Robert Israel_, Jan 10 2016
%t Table[MultiplicativeOrder[2^n, 2 n + 1], {n, 0, 100}]
%o (Magma) [1] cat [Modorder(2^n, 2*n+1): n in [1..100]];
%o (PARI) a(n) = if(n<0, 0, znorder(Mod(2^n, 2*n+1))); \\ _Altug Alkan_, Jan 04 2016
%o (GAP) List([0..100],n->OrderMod(2^n,2*n+1)); # _Muniru A Asiru_, Feb 25 2019
%Y Cf. A002326, A053447, A053451.
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Jan 03 2016