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A050384 Nonprimes such that n and phi(n) are relatively prime. 12
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 phi(n) is strongly prime to n. The a(n) are the strongly cyclic numbers apart from a(1). - Peter Luschny, Nov 14 2018
LINKS
Peter Luschny, Strong coprimality, 2011.
MAPLE
isStrongPrimeTo := (n, k) -> (igcd(n, k) = 1) and not (irem(n-1, k) = 0):
isStrongCyclic := n -> isStrongPrimeTo(n, numtheory:-phi(n)):
[1, op(select(isStrongCyclic, [$(2..404)]))]; # Peter Luschny, Dec 13 2021
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(n-1)
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, A181837.
Sequence in context: A339562 A338468 A337984 * A142862 A053343 A068081
KEYWORD
nonn
AUTHOR
Christian G. Bower, Nov 15 1999
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)