A243905 Multiplicative order of 2 modulo prime(n)^2 for n >= 2.

6, 20, 21, 110, 156, 136, 342, 253, 812, 155, 1332, 820, 602, 1081, 2756, 3422, 3660, 4422, 2485, 657, 3081, 6806, 979, 4656, 10100, 5253, 11342, 3924, 3164, 889, 17030, 9316, 19182, 22052, 2265, 8164, 26406, 13861, 29756, 31862, 32580, 18145, 18528, 38612

Offset: 2

Author

Felix Fröhlich, Jun 14 2014

Keywords

• nonn

Comments

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.

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

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A001220, A014664.

Programs

Maple

seq(numtheory:-order(2, ithprime(i)^2), i=2..1000); # Robert Israel, Jul 08 2014

Mathematica

Table[MultiplicativeOrder[2, Prime[n]^2], {n, 2, 100}] (* Jean-François Alcover, Jul 08 2014 *)

PARI

forprime(p=3, 10^2, print1(znorder(Mod(2, p^2)), ", "))

Formula

a(n) = prime(n)*A014664(n) for all odd primes that are not Wieferich. - Thomas Ordowski, Feb 04 2019