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 A141390 Overpseudoprimes of base 5. 2

%I

%S 781,1541,5461,13021,15751,25351,29539,38081,40501,79381,100651,

%T 121463,133141,195313,216457,315121,318551,319507,326929,341531,

%U 353827,375601,416641,432821,432821,453331,464881,498451,555397,556421,753667,764941,863329,872101

%N Overpseudoprimes of base 5.

%C 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.

%D Vladimir Shevelev, Gilberto Garcia-Pulgarin, Juan Miguel Velasquez-Soto and John 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

%H V. Shevelev, <a href="http://arxiv.org/abs/0806.3412">Overpseudoprimes, Mersenne Numbers and Wieferich Primes</a>, arXiv:0806.3412v8 [math.NT]

%Y Cf. A141232, A141350, A020231, A020229.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Jun 29 2008

%E Inserted a(2) and a(8) and extended at the suggestion of Gilberto Garcia-Pulgarin by _Vladimir Shevelev_, Feb 06 2012

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