

A050384


Nonprimes such that n and phi(n) are relatively prime.


10



1, 15, 33, 35, 51, 65, 69, 77, 85, 87, 91, 95, 115, 119, 123, 133, 141, 143, 145, 159, 161, 177, 185, 187, 209, 213, 215, 217, 221, 235, 247, 249, 255, 259, 265, 267, 287, 295, 299, 303, 319, 321, 323, 329, 335, 339, 341, 345, 365, 371, 377, 391, 393, 395, 403
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Also nonprimes n such that there is only one group of order n, i.e., A000001(n) = 1.
Intersection of A018252 and A003277.
Also numbers n such that n and A051953(n) are relatively prime.  Labos Elemer
Apart from the first term, this is a subsequence of A024556.  Charles R Greathouse IV, Apr 15 2015
Every Carmichael number and each of its nonprime divisors is in this sequence.  Emmanuel Vantieghem, Apr 20 2015
An alternative definition (excluding the 1): k is strongly prime to n <=> k is prime to n and k does not divide n  1 (cf. A181830). n is cyclic if n is prime to phi(n). n is strongly cyclic if n is strongly prime to phi(n). The a(n) are the strongly cyclic numbers apart from a(1).  Peter Luschny, Nov 14 2018


LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000


MATHEMATICA

Select[Range[450], !PrimeQ[#] && GCD[#, EulerPhi[#]] == 1&] (* Harvey P. Dale, Jan 31 2011 *)


PROG

(PARI) is(n)=!isprime(n) && gcd(eulerphi(n), n)==1 \\ Charles R Greathouse IV, Apr 15 2015
(Sage)
def isStrongPrimeTo(n, m): return gcd(n, m) == 1 and not m.divides(n1)
def isStrongCyclic(n): return isStrongPrimeTo(n, euler_phi(n))
[1] + [n for n in (1..403) if isStrongCyclic(n)] # Peter Luschny, Nov 14 2018


CROSSREFS

If the primes are included we get A003277. Cf. A000001, A000010 (phi), A181830.
Sequence in context: A339562 A338468 A337984 * A142862 A053343 A068081
Adjacent sequences: A050381 A050382 A050383 * A050385 A050386 A050387


KEYWORD

nonn


AUTHOR

Christian G. Bower, Nov 15 1999


STATUS

approved



