A178813 -id:A178813 - cp's OEIS frontend

A178812 (2^(p-1) - 1)/p^2 modulo prime p, if p^2 divides 2^(p-1) - 1.

487, 51

Offset: 1

Jonathan Sondow, Jun 16 2010

(2^(p-1) - 1)/p^2 modulo p, where p is a Wieferich prime A001220.
(2^(p-1) - 1)/p^2 modulo p, if prime p divides the Fermat quotient (2^(p-1) - 1)/p.
See A001220 for references, links, and additional comments.

			a(1) = 487 as the first Wieferich prime is 1093 and (2^1092 - 1)/1093^2 == 487 (mod 1093).
The 2nd Wieferich prime is 3511 and (2^3510 - 1)/3511^2 == 51 (mod 3511), so a(2) = 51.

Cf. A001220, A178813.

a(n) = (2^(p-1) - 1)/p^2 modulo p, where p = A001220(n).

a(1) = A178813(1).

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

Original entry on oeis.org

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

Jonathan Sondow, Jun 17 2010

(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.

			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.

Wikipedia, Generalized Wieferich primes

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

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).

cp's OEIS Frontend

A178812 (2^(p-1) - 1)/p^2 modulo prime p, if p^2 divides 2^(p-1) - 1.

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