

A141390


Overpseudoprimes of base 5.


2



781, 1541, 5461, 13021, 15751, 25351, 29539, 38081, 40501, 79381, 100651, 121463, 133141, 195313, 216457, 315121, 318551, 319507, 326929, 341531, 353827, 375601, 416641, 432821, 432821, 453331, 464881, 498451, 555397, 556421, 753667, 764941, 863329, 872101
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OFFSET

1,1


COMMENTS

If h_5(n) is the multiplicative order of 5 modulo n, r_5(n) is the number of cyclotomic cosets of 5 modulo n then, by the definition, n is an overpseudoprime of base 5 if h_5(n)*r_5(n)+1=n. These numbers are in A020231. In particular, if n is squarefree such that its prime factorization is n=p_1*...*p_k, then n is overpseudoprime of base 5 iff h_5(p_1)=...=h_5(p_k). E.g. since h_5(101)=h_5(251)=h_5(401)=25, the number 101*251*401=10165751 is in the sequence.


LINKS

Table of n, a(n) for n=1..34.
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, A141350, A020231, A020229.
Sequence in context: A139400 A115467 A020231 * A038477 A236888 A006113
Adjacent sequences: A141387 A141388 A141389 * A141391 A141392 A141393


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Jun 29 2008


EXTENSIONS

Inserted a(2) and a(8) and extended at the suggestion of Gilberto GarciaPulgarin by Vladimir Shevelev, Feb 06 2012


STATUS

approved



