login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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(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.

Sequence in context: A154369 A243592 A089966 * A142862 A053343 A068081

Adjacent sequences:  A050381 A050382 A050383 * A050385 A050386 A050387

KEYWORD

nonn

AUTHOR

Christian G. Bower, Nov 15 1999

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 27 07:44 EDT 2019. Contains 323599 sequences. (Running on oeis4.)