The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A328664 Least super pseudoprime to base n that is not a semiprime. 1
 294409, 7381, 13981, 342271, 9331, 747289, 63, 8, 99, 4921, 1729, 12, 195, 355957, 255, 8, 325, 18, 399, 20, 483, 1183, 575, 8, 27, 1729, 27, 28, 637, 30, 1023, 8, 105, 153, 1295, 12, 1105, 29659, 1599, 8, 12167, 42, 45, 44, 45, 1105, 637, 8, 147, 50, 2703, 27 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS 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. The semiprime Fermat pseudoprimes are trivial terms since they do not have composite proper divisors. REFERENCES 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. LINKS Amiram Eldar, Table of n, a(n) for n = 2..10000 J. Fehér and P. Kiss, Note on super pseudoprime numbers, Ann. Univ. Sci. Budapest, Eötvös Sect. Math., Vol. 26 (1983), pp. 157-159, entire volume. 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, entire volume. Andrzej Rotkiewicz, Solved and unsolved problems on pseudoprime numbers and their generalizations, Applications of Fibonacci numbers, Springer, Dordrecht, 1999, pp. 293-306. Lawrence Somer, On superpseudoprimes, Mathematica Slovaca, Vol. 54, No. 5 (2004), pp. 443-451. EXAMPLE a(2) = 294409 = 37 * 73 * 109 is the first term of A178997. a(3) = 7381 = 11^2 * 61 is the first term of A328663. MATHEMATICA a[n_] := Module[{k=1}, While[PrimeOmega[k] < 3 || !AllTrue[Rest[Divisors[k]], PowerMod[n, #-1, #] == 1 &], k++]; k]; Array[a, 10, 2] CROSSREFS Cf. A178997, A328662, A328663. Sequence in context: A158124 A050249 A224973 * A328935 A182206 A178997 Adjacent sequences:  A328661 A328662 A328663 * A328665 A328666 A328667 KEYWORD nonn AUTHOR Amiram Eldar, Oct 24 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 19 00:40 EST 2020. Contains 331030 sequences. (Running on oeis4.)