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%I #8 Oct 25 2019 05:01:27
%S 294409,7381,13981,342271,9331,747289,63,8,99,4921,1729,12,195,355957,
%T 255,8,325,18,399,20,483,1183,575,8,27,1729,27,28,637,30,1023,8,105,
%U 153,1295,12,1105,29659,1599,8,12167,42,45,44,45,1105,637,8,147,50,2703,27
%N Least super pseudoprime to base n that is not a semiprime.
%C A number is super pseudoprime to base n > 1 if it is a Fermat pseudoprime to base n and of whose divisors that are larger than 1 are either primes or Fermat pseudoprimes to base n.
%C The semiprime Fermat pseudoprimes are trivial terms since they do not have composite proper divisors.
%D Michal Krížek, Florian Luca, and Lawrence Somer, 17 Lectures on Fermat Numbers: From Number Theory to Geometry, Springer-Verlag, New York, 2001, chapter 12, Fermat's Little Theorem, Pseudoprimes, and Superpseudoprimes, pp. 130-146.
%H Amiram Eldar, <a href="/A328664/b328664.txt">Table of n, a(n) for n = 2..10000</a>
%H J. Fehér and P. Kiss, Note on super pseudoprime numbers, Ann. Univ. Sci. Budapest, Eötvös Sect. Math., Vol. 26 (1983), pp. 157-159, <a href="http://annalesm.elte.hu/annales26-1983/Annales_1983_T-XXVI.pdf">entire volume</a>.
%H B. M. Phong, On super pseudoprimes which are products of three primes, Ann. Univ. Sci. Budapest. Eótvós Sect. Math., Vol. 30 (1987), pp. 125-129, <a href="http://annalesm.elte.hu/annales30-1987/Annales_1987_T-XXX.pdf">entire volume</a>.
%H Andrzej Rotkiewicz, <a href="https://doi.org/10.1007/978-94-011-4271-7_28">Solved and unsolved problems on pseudoprime numbers and their generalizations</a>, Applications of Fibonacci numbers, Springer, Dordrecht, 1999, pp. 293-306.
%H Lawrence Somer, <a href="https://dml.cz/handle/10338.dmlcz/130094">On superpseudoprimes</a>, Mathematica Slovaca, Vol. 54, No. 5 (2004), pp. 443-451.
%e a(2) = 294409 = 37 * 73 * 109 is the first term of A178997.
%e a(3) = 7381 = 11^2 * 61 is the first term of A328663.
%t a[n_] := Module[{k=1}, While[PrimeOmega[k] < 3 || !AllTrue[Rest[Divisors[k]], PowerMod[n, #-1, #] == 1 &], k++]; k]; Array[a, 10, 2]
%Y Cf. A178997, A328662, A328663.
%K nonn
%O 2,1
%A _Amiram Eldar_, Oct 24 2019
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