

A141350


Overpseudoprimes of base 3.


4



121, 703, 3281, 8401, 12403, 31621, 44287, 47197, 55969, 74593, 79003, 88573, 97567, 105163, 112141, 211411, 221761, 226801, 228073, 293401, 313447, 320167, 328021, 340033, 359341, 432821, 443713, 453259, 478297, 497503, 504913, 679057, 709873, 801139, 867043, 894781, 973241, 1042417
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OFFSET

1,1


COMMENTS

If h_3(n) is the multiplicative order of 3 modulo n, r_3(n) is the number of cyclotomic cosets of 3 modulo n then, by the definition, n is an overpseudoprime of base 3 if h_3(n)*r_3(n)+1=n. These numbers are in A020229.
In particular, if n is squarefree such that its prime factorization is n=p_1*...*p_k, then n is overpseudoprime of base 3 iff h_3(p_1)=...=h_3(p_k).


LINKS

Table of n, a(n) for n=1..38.
V. Shevelev, Overpseudoprimes, Mersenne Numbers and Wieferich Primes, arXiv:0806.3412 [math.NT], 20082012.
V. Shevelev, G. GarciaPulgarin, J. M. Velasquez and J. H. Castillo, Overpseudoprimes, and Mersenne and Fermat numbers as primover numbers, arXiv preprint arXiv:1206:0606, 2012.  From N. J. A. Sloane, Oct 28 2012
V. Shevelev, G. GarciaPulgarin, J. M. Velasquez and J. H. Castillo, Overpseudoprimes, and Mersenne and Fermat Numbers as Primover Numbers, J. Integer Seq. 15 (2012) Article 12.7.7.


CROSSREFS

Cf. A141232, A137576, A001262, A020229, A062117, A006694.
Sequence in context: A262051 A048950 A020229 * A235408 A190877 A238250
Adjacent sequences: A141347 A141348 A141349 * A141351 A141352 A141353


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Jun 27 2008, corrected Sep 07 2008


EXTENSIONS

a(10)a(38) from Gilberto GarciaPulgarin  Vladimir Shevelev, Feb 06 2012


STATUS

approved



