

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
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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 (39.713) 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



