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A322937 Triangular array in which the n-th row lists the primes strongly prime to n (in ascending order). For the empty rows n = 1, 2, 3, 4 and 6 we set by convention 0.

%I A322937 #22 Apr 02 2019 17:53:32
%S A322937 0,0,0,0,3,0,5,3,5,5,7,7,3,7,5,7,5,7,11,3,5,11,11,13,7,11,13,3,5,7,11,
%T A322937 13,5,7,11,13,5,7,11,13,17,3,7,11,13,17,11,13,17,19,5,13,17,19,3,5,7,
%U A322937 13,17,19,5,7,11,13,17,19,7,11,13,17,19,23
%N A322937 Triangular array in which the n-th row lists the primes strongly prime to n (in ascending order). For the empty rows n = 1, 2, 3, 4 and 6 we set by convention 0.
%C A322937 A number k is strongly prime to n if and only if k <= n is prime to n and k does not divide n-1. See the link to 'Strong Coprimality'. (Our terminology follows the plea of Knuth, Graham and Patashnik in Concrete Mathematics, p. 115.)
%H A322937 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/StrongCoprimality">Strong Coprimality</a>
%e A322937 The length of row n is A181834(n). The triangular array starts:
%e A322937 [1] {}
%e A322937 [2] {}
%e A322937 [3] {}
%e A322937 [4] {}
%e A322937 [5] {3}
%e A322937 [6] {}
%e A322937 [7] {5}
%e A322937 [8] {3, 5}
%e A322937 [9] {5, 7}
%e A322937 [10] {7}
%e A322937 [11] {3, 7}
%e A322937 [12] {5, 7}
%e A322937 [13] {5, 7, 11}
%e A322937 [14] {3, 5, 11}
%e A322937 [15] {11, 13}
%e A322937 [16] {7, 11, 13}
%e A322937 [17] {3, 5, 7, 11, 13}
%e A322937 [18] {5, 7, 11, 13}
%e A322937 [19] {5, 7, 11, 13, 17}
%e A322937 [20] {3, 7, 11, 13, 17}
%p A322937 Primes := n -> select(isprime, {$1..n}):
%p A322937 StrongCoprimes := n -> select(k->igcd(k, n)=1, {$1..n}) minus numtheory:-divisors(n-1):
%p A322937 StrongCoprimePrimes := n -> Primes(n) intersect StrongCoprimes(n):
%p A322937 A322937row := proc(n) if n in {1, 2, 3, 4, 6} then return 0 else op(StrongCoprimePrimes(n)) fi end:
%p A322937 seq(A322937row(n), n=1..25);
%t A322937 Table[Select[Prime@ Range@ PrimePi@ n, And[GCD[#, n] == 1, Mod[n - 1, #] != 0] &] /. {} -> {0}, {n, 25}] // Flatten (* _Michael De Vlieger_, Apr 01 2019 *)
%o A322937 (Sage)
%o A322937 def primes_primeto(n):
%o A322937     return [p for p in prime_range(n) if gcd(p, n) == 1]
%o A322937 def primes_strongly_primeto(n):
%o A322937     return [p for p in set(primes_primeto(n)) - set((n-1).divisors())]
%o A322937 def A322937row(n):
%o A322937     if n in [1, 2, 3, 4, 6]: return [0]
%o A322937     return sorted(primes_strongly_primeto(n))
%o A322937 for n in (1..25): print(A322937row(n))
%Y A322937 Cf. A000010, A038566, A181831, A181832, A181833, A181834, A181835, A181836, A322936.
%K A322937 nonn,tabf
%O A322937 1,5
%A A322937 _Peter Luschny_, Apr 01 2019