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A050384
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Nonprimes such that n and phi(n) are relatively prime.
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12
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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
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OFFSET
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1,2
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COMMENTS
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Also nonprimes n such that there is only one group of order n, i.e., A000001(n) = 1.
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
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LINKS
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MAPLE
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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
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MATHEMATICA
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Select[Range[450], !PrimeQ[#] && GCD[#, EulerPhi[#]] == 1&] (* Harvey P. Dale, Jan 31 2011 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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