login
2^(n-1) mod n^2.
2

%I #29 Jul 11 2014 14:50:12

%S 0,2,4,8,16,32,15,0,13,12,56,32,40,156,184,0,222,176,58,288,319,464,

%T 392,320,341,496,40,64,30,212,187,0,301,308,9,1040,38,952,472,1088,

%U 944,1544,1076,800,391,508,2069,2048,1191,1312,922,2608,1909,284,2359

%N 2^(n-1) mod n^2.

%C If p is a Wieferich prime, then a(p) = 1, that is, a(A001220(n)) = 1.

%C a(n) = 0 iff n = 1 or n = 2^k (k >= 3).

%C a(n) = 1 iff n is either a Wieferich prime or a Wieferich pseudoprime (i.e. a composite c such that c-1 is in A240719). - _Felix Fröhlich_, Jul 11 2014

%H T. D. Noe, <a href="/A220105/b220105.txt">Table of n, a(n) for n = 1..10000</a>

%e a(7) = 2^(7-1) mod 7^2 = 64 mod 49 = 15.

%t Table[PowerMod[2, n - 1, n^2], {n, 100}] (* _T. D. Noe_, Dec 17 2012 *)

%Y Cf. A001220, A062173.

%K nonn

%O 1,2

%A _Franz Vrabec_, Dec 17 2012