A220105 2^(n-1) mod n^2.

0, 2, 4, 8, 16, 32, 15, 0, 13, 12, 56, 32, 40, 156, 184, 0, 222, 176, 58, 288, 319, 464, 392, 320, 341, 496, 40, 64, 30, 212, 187, 0, 301, 308, 9, 1040, 38, 952, 472, 1088, 944, 1544, 1076, 800, 391, 508, 2069, 2048, 1191, 1312, 922, 2608, 1909, 284, 2359

Offset: 1

Author

Franz Vrabec, Dec 17 2012

Keywords

• nonn

Comments

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

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

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

Examples

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

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001220, A062173.

Programs

Mathematica

Table[PowerMod[2, n - 1, n^2], {n, 100}] (* T. D. Noe, Dec 17 2012 *)