A178814 (n^(p-1) - 1)/p^2 mod p, where p is the first prime that divides (n^(p-1) - 1)/p.

0, 487, 4, 974, 1, 30384, 1, 1, 0, 2, 46, 1571, 1, 17, 24160, 855, 0, 4, 1, 189, 1, 5, 11, 1, 0, 0, 1, 0, 1, 3, 2, 3, 0, 19632919407, 1, 60768, 1, 11, 1435, 8, 0, 0, 2, 2, 1, 1

Offset: 1

Author

Jonathan Sondow, Jun 17 2010

Keywords

• hard
• more
• nonn

Comments

(n^(p-1) - 1)/p^2 mod p, where p is the first prime such that p^2 divides n^(p-1) - 1.

See references and additional comments, links, and cross-refs in A001220 and A039951.

Examples

			The first prime p that divides (3^(p-1) - 1)/p is 11, so a(3) = (3^10 - 1)/11^2 mod 11 = 488 mod 11 = 4.
		

Links

• Wikipedia, Generalized Wieferich primes

Crossrefs

a(2) = A178812(1) = A178813(1). Cf. A001220, A039951, A174422.

Formula

a(n) = (n^(p-1) - 1)/p^2 mod p, where p = A039951(n).

a(n) = k mod 2, if n = 4k+1.

a(prime(n)) = A178813(n).