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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 (list; graph; refs; listen; history; text; internal format)
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], 2008-2012.

V. Shevelev, G. Garcia-Pulgarin, 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. Garcia-Pulgarin, 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 Garcia-Pulgarin by Vladimir Shevelev, Feb 06 2012

STATUS

approved

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Last modified August 23 04:06 EDT 2017. Contains 290958 sequences.