A122414 Triangle T(n,k) for 1 <= k <= n read by rows, where T(n,k) = 1 if gcd(n,k) is prime, 0 otherwise.

0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0

Offset: 1

Author

Klaus Brockhaus, Sep 03 2006

Keywords

• nonn
• tabl
• easy

Examples

			The triangle starts
  0
  0 1
  0 0 1
  0 1 0 0
  0 0 0 0 1
  0 1 1 1 0 0
  0 0 0 0 0 0 1
  0 1 0 0 0 1 0 0
  0 0 1 0 0 1 0 0 0
  0 1 0 1 1 1 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 1
  0 1 1 0 0 0 0 0 1 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 1
  0 1 0 1 0 1 1 1 0 1 0 1 0 0
  0 0 1 0 1 1 0 0 1 1 0 1 0 0 0
		

Crossrefs

Cf. A010051 (diagonal), A122415 (sub-triangle).

Row sums are in A117494. [From Klaus Brockhaus, May 29 2009]

Programs

Maple

A122414 := proc(n,k)
    if isprime(igcd(n,k)) then
        1;
    else
        0;
    end if;
end proc: # R. J. Mathar, Apr 21 2021

Mathematica

row[n_] := Boole[PrimeQ[GCD[n, Range[n]]]]; Array[row, 14] // Flatten (* Amiram Eldar, May 23 2025 *)

PARI

{m=14; v=vector(m,x,vector(x)); for(n=1,m,for(k=1,n,if(isprime(gcd(n,k)),v[n][k]=1))); for(n=1,m,for(k=1,n,print1(v[n][k],",")))}

Formula

T(n,n) = A010051(n).

T(n,1) = 0.