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

3,1

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A038566, A048865, A053669.

Sequence in context: A249049 A138239 A361330 * A174063 A327277 A124459

Adjacent sequences: A112481 A112482 A112483 * A112485 A112486 A112487

Keyword

nonn,tabf

Author

Leroy Quet, Dec 13 2005

Extensions

Extended by Ray Chandler, Dec 26 2005

Status

approved