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

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, 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, 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

Offset: 3

Author

Leroy Quet, Dec 13 2005

Keywords

• nonn
• tabf

Comments

Array's n-th row contains A048865(n) terms.

T(A005408(n),1) = 2; T(n,1) = A053669(n). - Reinhard Zumkeller, Sep 23 2011

These are the primes in row n >= 3 of A038566 (smallest positive restricted residue system modulo n). - Wolfdieter Lang, Jan 18 2017

Examples

			Row 9 is [2, 5, 7], since 2, 5 and 7 are the primes < 9 and coprime to 9.
The irregular triangle begins:
n\k 1 2  3  4  5  6  7  8 ...
3:  2
4:  3
5:  2 3
6:  5
7:  2 3  5
8:  3 5  7
9:  2 5  7
10: 3 7
11: 2 3  5  7
12: 5 7 11
13: 2 3  5  7 11
14: 3 5 11 13
15: 2 7 11 13
16: 3 5  7 11 13
17: 2 3  5  7 11 13
18: 5 7 11 13 17
19: 2 3  5  7 11 13 17
20: 3 7 11 13 17 19
21: 2 5 11 13 17 19
22: 3 5  7 13 17 19
23: 2 3  5  7 11 13 17 19
... - _Wolfdieter Lang_, Jan 18 2017
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 3..16603 (rows 3 <= n <= 400).

Crossrefs

Cf. A038566, A048865, A053669.

Programs

Mathematica

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 *)
Table[Complement[Prime@ Range@ PrimePi@ n, FactorInteger[n][[All, 1]]], {n, 3, 23}] // Flatten (* Michael De Vlieger, Sep 04 2017 *)

Python

from sympy import primerange, gcd
def a(n): return [i for i in primerange(1, n) if gcd(i, n)==1]
for n in range(3, 24): print(a(n)) # Indranil Ghosh, Apr 27 2017

Extensions

Extended by Ray Chandler, Dec 26 2005