This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A141350 #30 Jun 25 2019 01:47:04 %S A141350 121,703,3281,8401,12403,31621,44287,47197,55969,74593,79003,88573, %T A141350 97567,105163,112141,211411,221761,226801,228073,293401,313447,320167, %U A141350 328021,340033,359341,432821,443713,453259,478297,497503,504913,679057,709873,801139,867043,894781,973241,1042417 %N A141350 Overpseudoprimes to base 3. %C A141350 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 to base 3 if h_3(n)*r_3(n)+1=n. These numbers are in A020229. %C A141350 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). %H A141350 Amiram Eldar, <a href="/A141350/b141350.txt">Table of n, a(n) for n = 1..10798</a> (calculated using the b-file at A020229) %H A141350 V. Shevelev, <a href="http://arxiv.org/abs/0806.3412">Overpseudoprimes, Mersenne Numbers and Wieferich Primes</a>, arXiv:0806.3412 [math.NT], 2008-2012. %H A141350 V. Shevelev, G. Garcia-Pulgarin, J. M. Velasquez and J. H. Castillo, <a href="http://arxiv.org/abs/1206.0606">Overpseudoprimes, and Mersenne and Fermat numbers as primover numbers</a>, arXiv preprint arXiv:1206:0606 [math.NT], 2012. - From _N. J. A. Sloane_, Oct 28 2012 %H A141350 V. Shevelev, G. Garcia-Pulgarin, J. M. Velasquez and J. H. Castillo, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL15/Shevelev/shevelev19.html">Overpseudoprimes, and Mersenne and Fermat Numbers as Primover Numbers</a>, J. Integer Seq. 15 (2012) Article 12.7.7. %t A141350 ops3Q[n_] := CompositeQ[n] && GCD[n, 3] == 1 && MultiplicativeOrder[3, n]*(DivisorSum[n, EulerPhi[#]/MultiplicativeOrder[3, #] &] - 1) + 1 == n; Select[Range[10^6], ops3Q] (* _Amiram Eldar_, Jun 24 2019 *) %o A141350 (PARI) isok(n) = (n!=1) && !isprime(n) && (gcd(n,3)==1) && (znorder(Mod(3,n)) * (sumdiv(n, d, eulerphi(d)/znorder(Mod(3, d))) - 1) + 1 == n); \\ _Michel Marcus_, Oct 25 2018 %Y A141350 Cf. A141232, A137576, A001262, A020229, A062117, A006694. %K A141350 nonn %O A141350 1,1 %A A141350 _Vladimir Shevelev_, Jun 27 2008, corrected Sep 07 2008 %E A141350 a(10)-a(38) from Gilberto Garcia-Pulgarin added by _Vladimir Shevelev_, Feb 06 2012