A247154 a(n) = smallest composite c such that n^(A000010(c)) == 1 (mod c^2), i.e., smallest composite Wieferich number to base n.

4, 3279, 22, 3279, 41542, 330805, 4, 3279, 4, 1461, 142, 1812389, 1726, 3883, 4, 3279, 4, 35, 6, 1967

Offset

1,1

Comments

a(21) > 10^9

a(22)-a(28): 39, 4, 128165, 4, 9, 22, 9

a(29) > 10^9

a(30)-a(33): 1123787, 4, 3279, 4

a(34) > 10^9

Links

Table of n, a(n) for n=1..20.

William D. Banks, Florian Luca, Igor E. Shparlinski, Estimates for Wieferich numbers, The Ramanujan Journal, December 2007, Volume 14, Issue 3, pp 361-378.

Takashi Agoh, Karl Dilcher, Ladislav Skula, Fermat Quotients for Composite Moduli, Journal of Number Theory, September 1997, Volume 66, Issue 1, pp 29-50.

Prog

(PARI) for(n=1, 20, forcomposite(c=1, 1e9, if(Mod(n, c^2)^(eulerphi(c))==1, print1(c, ", "); next({2}))); print1("--, "))

Crossrefs

Cf. A039951, A077816, A241977, A241978, A242958, A242959, A242960, A245529.

Sequence in context: A132639 A132643 A079193 * A134908 A114498 A069120

Adjacent sequences: A247151 A247152 A247153 * A247155 A247156 A247157

Keyword

nonn,more

Author

Felix Fröhlich, Nov 21 2014

Status

approved