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A066651 Primes of the form 2*s + 1, where s is a squarefree number (A005117). 2
3, 5, 7, 11, 13, 23, 29, 31, 43, 47, 53, 59, 61, 67, 71, 79, 83, 103, 107, 131, 139, 149, 157, 167, 173, 179, 191, 211, 223, 227, 229, 239, 263, 269, 277, 283, 293, 311, 317, 331, 347, 349, 359, 367, 373, 383, 389, 419, 421, 431 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For these odd primes delta(p) = A055034(n) = (p-1)/2 is squarefree, and therefore the (Abelian) multiplicative group Modd p (see a comment on A203571 for Modd n, not to be confused with mod n) is guaranteed to be cyclic. This is because the number of Abelian groups of order n (A000688) is 1 precisely for the squarefree numbers A005117. See also A210845. One can in fact prove that the multiplicative group Modd p is cyclic for all primes (the case p=2 is trivial).  [From Wolfdieter Lang, Sep 24 2012]

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

a(13) = A000040(18) = 61 = 2*30+1 = 2*A005117(19)+1.

CROSSREFS

Cf. A005385, A066652, A066653.

Sequence in context: A174350 A240476 A040140 * A182583 A181741 A154319

Adjacent sequences:  A066648 A066649 A066650 * A066652 A066653 A066654

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jan 10 2002

STATUS

approved

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Last modified September 20 03:55 EDT 2019. Contains 327212 sequences. (Running on oeis4.)