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

Author

Felix Fröhlich, Nov 21 2014

Keywords

• nonn
• more

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

• 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.

Crossrefs

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

Programs

PARI

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