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 A327823 Odd integers m such that every odd integer k with 1 < k < m and gcd(k,m) = 1 is prime. 0
 1, 3, 5, 7, 9, 15, 21, 45, 105 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Solomon W. Golomb and Kee-Wai Lau prove in AMM (see link) that the greatest odd integer with this property is 105. This sequence is inspirated by the other one: integers q such that every integer k with 1 < k < q and gcd(k,q) = 1 is prime, with 2, 3, 4, 6, 8, 12, 18, 24, 30 in A048597 \ {1}. The terms 1 and 3 are added after recommendations of Amiram Eldar and Michel Marcus. REFERENCES David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, Penguin Books, London, England, 1997, number 105, page 118. LINKS Solomon W. Golomb and Kee-Wai Lau, Problem E3137, American Mathematical Monthly, Vol. 94, No. 9, Nov. 1987, pp. 883-884. EXAMPLE For m = 15 and 1 < k odd < 15, we have gcd(3,15) = 3, gcd(5,15) = 5, gcd(7,15) = 1, gcd(9,15) = 3, gcd(11,15) = 1, gcd(13,15) = 1. So, gcd(k,15) = 1 only if k is prime and 15 is a term. For m = 63, we have gcd(25,63) = 1 with 25 no prime, so 63 is not a term. MATHEMATICA aQ[n_] := OddQ[n] && AllTrue[Select[Range[3, n, 2], CoprimeQ[n, #] &], PrimeQ]; Select[Range[10^3], aQ] (* Amiram Eldar, Sep 27 2019 *) PROG (PARI) isok(m) = {if (m % 2, forstep (k=3, m-1, 2, if ((gcd(k, m) == 1) && !isprime(k), return(0)); ); return(1); ); } \\ Michel Marcus, Sep 27 2019 CROSSREFS Cf. A048597. Sequence in context: A201643 A018388 A100866 * A102633 A052942 A240944 Adjacent sequences:  A327820 A327821 A327822 * A327824 A327825 A327826 KEYWORD nonn,full,fini AUTHOR Bernard Schott, Sep 26 2019 STATUS approved

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Last modified January 21 16:47 EST 2020. Contains 331114 sequences. (Running on oeis4.)