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 A193305 Composite numbers of the form 4, p^m, or 2*p^m for p an odd prime. All composites that have a primitive root. 3
 4, 6, 9, 10, 14, 18, 22, 25, 26, 27, 34, 38, 46, 49, 50, 54, 58, 62, 74, 81, 82, 86, 94, 98, 106, 118, 121, 122, 125, 134, 142, 146, 158, 162, 166, 169, 178, 194, 202, 206, 214, 218, 226, 242, 243, 250, 254, 262, 274, 278, 289, 298, 302, 314, 326, 334, 338, 343 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Nonprime n such that the multiplicative group modulo n is cyclic.  Nonprime terms of A033948 (omitting the initial term 1). - Joerg Arndt, Aug 07 2011 a(n) has a primitive root for any n. - Arkadiusz Wesolowski, Sep 06 2012 See, e.g., the Niven et al. reference. - Wolfdieter Lang, Jan 18 2017 REFERENCES Ivan Niven, Herbert S. Zuckerman and Hugh L. Montgomery, An Introduction to the Theory Of Numbers, Fifth Edition, John Wiley and Sons, Inc., NY 1991, Theorem 2.41, p. 104. LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Joerg Arndt, Matters Computational (The Fxtbook), relation (39.7-13) on page 779. MATHEMATICA lim = 500; t = {4}; Do[p = Prime[n]; k = 1; While[p^k <= lim, If[k > 1, AppendTo[t, p^k]]; If[2*p^k <= lim, AppendTo[t, 2*p^k]]; k++], {n, 2, PrimePi[lim/2]}]; Sort[t]; (* T. D. Noe, Sep 06 2012 *) PROG (PARI) for (n=2, 555, if ( isprime(n), next() ); if ( 1 == #(znstar(n)[3]), print1(n, ", ") ); );  /* Joerg Arndt, Aug 07 2011 */ CROSSREFS Cf. A033948, A033949 (composites without primitive root). A279398. Sequence in context: A115652 A317299 A236026 * A084759 A054395 A142863 Adjacent sequences:  A193302 A193303 A193304 * A193306 A193307 A193308 KEYWORD nonn AUTHOR Warren Breslow, Jul 21 2011 EXTENSIONS More terms from Joerg Arndt, Aug 07 2011 Name corrected, and augmented by Wolfdieter Lang, Jan 18 2017 STATUS approved

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Last modified December 11 12:33 EST 2019. Contains 329916 sequences. (Running on oeis4.)