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A112484 Array where n-th row contains the primes < n and coprime to n.

%I A112484 #33 May 02 2021 21:43:16
%S A112484 2,3,2,3,5,2,3,5,3,5,7,2,5,7,3,7,2,3,5,7,5,7,11,2,3,5,7,11,3,5,11,13,
%T A112484 2,7,11,13,3,5,7,11,13,2,3,5,7,11,13,5,7,11,13,17,2,3,5,7,11,13,17,3,
%U A112484 7,11,13,17,19,2,5,11,13,17,19,3,5,7,13,17,19,2,3,5,7,11,13,17,19,5,7,11,13
%N A112484 Array where n-th row contains the primes < n and coprime to n.
%C A112484 Array's n-th row contains A048865(n) terms.
%C A112484 T(A005408(n),1) = 2; T(n,1) = A053669(n). - _Reinhard Zumkeller_, Sep 23 2011
%C A112484 These are the primes in row n >= 3 of A038566 (smallest positive restricted residue system modulo n). - _Wolfdieter Lang_, Jan 18 2017
%H A112484 Michael De Vlieger, <a href="/A112484/b112484.txt">Table of n, a(n) for n = 3..16603</a> (rows 3 <= n <= 400).
%e A112484 Row 9 is [2, 5, 7], since 2, 5 and 7 are the primes < 9 and coprime to 9.
%e A112484 The irregular triangle begins:
%e A112484 n\k 1 2  3  4  5  6  7  8 ...
%e A112484 3:  2
%e A112484 4:  3
%e A112484 5:  2 3
%e A112484 6:  5
%e A112484 7:  2 3  5
%e A112484 8:  3 5  7
%e A112484 9:  2 5  7
%e A112484 10: 3 7
%e A112484 11: 2 3  5  7
%e A112484 12: 5 7 11
%e A112484 13: 2 3  5  7 11
%e A112484 14: 3 5 11 13
%e A112484 15: 2 7 11 13
%e A112484 16: 3 5  7 11 13
%e A112484 17: 2 3  5  7 11 13
%e A112484 18: 5 7 11 13 17
%e A112484 19: 2 3  5  7 11 13 17
%e A112484 20: 3 7 11 13 17 19
%e A112484 21: 2 5 11 13 17 19
%e A112484 22: 3 5  7 13 17 19
%e A112484 23: 2 3  5  7 11 13 17 19
%e A112484 ... - _Wolfdieter Lang_, Jan 18 2017
%t A112484 f[l_] := Block[{n}, n = Length[l] + 1; Return[Append[l, Select[Range[n - 1], PrimeQ[ # ] && Mod[n, # ] > 0 &]]];]; Flatten[Nest[f, {}, 24]] (* _Ray Chandler_, Dec 26 2005 *)
%t A112484 Table[Complement[Prime@ Range@ PrimePi@ n, FactorInteger[n][[All, 1]]], {n, 3, 23}] // Flatten (* _Michael De Vlieger_, Sep 04 2017 *)
%o A112484 (Python)
%o A112484 from sympy import primerange, gcd
%o A112484 def a(n): return [i for i in primerange(1, n) if gcd(i, n)==1]
%o A112484 for n in range(3, 24): print(a(n)) # _Indranil Ghosh_, Apr 27 2017
%Y A112484 Cf. A038566, A048865, A053669.
%K A112484 nonn,tabf
%O A112484 3,1
%A A112484 _Leroy Quet_, Dec 13 2005
%E A112484 Extended by _Ray Chandler_, Dec 26 2005