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%I #45 Mar 12 2019 04:50:18
%S 6,20,21,110,156,136,342,253,812,155,1332,820,602,1081,2756,3422,3660,
%T 4422,2485,657,3081,6806,979,4656,10100,5253,11342,3924,3164,889,
%U 17030,9316,19182,22052,2265,8164,26406,13861,29756,31862,32580,18145,18528,38612
%N Multiplicative order of 2 modulo prime(n)^2 for n >= 2.
%C p=prime(n) is in A001220 if and only if a(n) is equal to A014664(n). So far this is known to hold only for p=1093 and p=3511.
%C This happens for n=183 and 490, that is for p=prime(183)=1093 and p=prime(490)=3511, with values 364 and 1755 (see b-files). - _Michel Marcus_, Jun 29 2014
%C If 2^q-1 is p=prime(n), i.e., for n in A016027, then a(n)=pq and lpf(2^a(n)-1)=p. - _Thomas Ordowski_, Feb 04 2019
%H Charles R Greathouse IV, <a href="/A243905/b243905.txt">Table of n, a(n) for n = 2..10000</a>
%F a(n) = prime(n)*A014664(n) for all odd primes that are not Wieferich. - _Thomas Ordowski_, Feb 04 2019
%p seq(numtheory:-order(2, ithprime(i)^2), i=2..1000); # _Robert Israel_, Jul 08 2014
%t Table[MultiplicativeOrder[2, Prime[n]^2], {n, 2, 100}] (* _Jean-François Alcover_, Jul 08 2014 *)
%o (PARI) forprime(p=3, 10^2, print1(znorder(Mod(2, p^2)), ", "))
%Y Cf. A001220, A014664.
%K nonn
%O 2,1
%A _Felix Fröhlich_, Jun 14 2014
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