A282552 - OEIS

%I #10 Feb 27 2017 02:33:56

%S 4,16,18,100,144,128,324,242,784,150,1296,800,588,1058,2704,3364,3600,

%T 4356,2450,648,3042,6724,968,4608,10000,5202,11236,3888,3136,882,

%U 16900,9248,19044,21904,2250,8112,26244,13778,29584,31684,32400,18050,18432,38416

%N Difference between the multiplicative orders of 2 modulo p^2 and 2 modulo p, where p = prime(n).

%C a(n) = 0 iff A014664(n) = A243905(n), i.e., iff prime(n) is a Wieferich prime (A001220). So far this is known to be the case only for prime(183) = 1093 and prime(490) = 3511, i.e., a(183) = 0 and a(490) = 0.

%F a(n) = A243905(n) - A014664(n).

%t Table[MultiplicativeOrder[2, #^2] - MultiplicativeOrder[2, #] &@ Prime@ n, {n, 2, 45}] (* _Michael De Vlieger_, Feb 18 2017 *)

%o (PARI) a(n) = my(p=prime(n)); znorder(Mod(2, p^2)) - znorder(Mod(2, p))

%Y Cf. A001220, A014664, A243905.

%K nonn

%O 2,1

%A _Felix Fröhlich_, Feb 18 2017