The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A323214 Composite numbers k such that p^(k-1) == 1 (mod k) for every prime p strongly prime to k. 0
 4, 6, 561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, 41041, 46657, 52633, 62745, 63973, 75361, 101101, 115921, 126217, 162401, 172081, 188461, 252601, 278545, 294409, 314821, 334153, 340561, 399001, 410041, 449065, 488881, 512461, 530881, 552721 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A positive number k <= n is strongly prime to n if and only if k is prime to n and k does not divide n-1. See A322937 and the link to 'Strong Coprimality'. Apparently essentially the Carmichael numbers A002997. LINKS K. Bouallègue, O. Echi and R. G. E. Pinch, Korselt numbers and sets, International Journal of Number Theory, 6 (2010), 257-269. A. Korselt, G. Tarry, I. Franel and G. Vacca, Problème chinois, L'intermédiaire des mathématiciens 6 (1899), 142-144. Peter Luschny, Strong Coprimality C. Pomerance, J. L. Selfridge, and S. S. Wagstaff, Jr., The pseudoprimes to 25*10^9, Math. Comp., 35 (1980), 1003-1026. V. Šimerka, Zbytky z arithmetické posloupnosti, (On the remainders of an arithmetic progression), Časopis pro pěstování matematiky a fysiky. 14  (1885), 221-225. L. Wang, The Korselt set of a power of a prime, International Journal of Number Theory, 14 (2018), 233-240. EXAMPLE 2, 3 and 5 are not in this sequence because primes are not in this sequence. 4 and 6 are in this sequence because there are no primes strongly prime to 4 respectively 6. For n = 1729 there are 1296 test cases using the definition of A002997 but only 264 test cases using the definition of a(n). PROG (Sage) def is_strongCarmichael(n):     if n == 1 or is_prime(n): return False     for k in (1..n):         if is_prime(k) and not k.divides(n-1) and is_primeto(k, n):             if power_mod(k, n-1, n) != 1: return false     return true def A323214_list(len):     return [n for n in (1..len) if is_strongCarmichael(n)] print(A323214_list(600000)) (Julia) using IntegerSequences PrimesPrimeTo(n) = (p for p in Primes(n) if isPrimeTo(p, n)) function isStrongCarmichael(n)     if isComposite(n)         for k in PrimesPrimeTo(n)             if ! Divides(k, n-1)                 if powermod(k, n-1, n) != 1                     return false                 end             end         end         return true     end     return false end L323214(len) = [n for n in 1:len if isStrongCarmichael(n)] L323214(30000) |> println CROSSREFS Cf. A002997, A322937. Sequence in context: A056831 A027717 A035481 * A061214 A137024 A054264 Adjacent sequences:  A323211 A323212 A323213 * A323215 A323216 A323217 KEYWORD nonn AUTHOR Peter Luschny, Apr 01 2019 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.

Last modified January 16 18:17 EST 2022. Contains 350376 sequences. (Running on oeis4.)