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

1,1

Links

Table of n, a(n) for n=1..105.

Formula

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

T(n,1) = 0.

Example

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

Maple

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

Prog

(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], ", ")))}

Crossrefs

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

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

Sequence in context: A289128 A272664 A143518 * A288216 A189628 A289239

Adjacent sequences: A122411 A122412 A122413 * A122415 A122416 A122417

Keyword

nonn,tabl,easy

Author

Klaus Brockhaus, Sep 03 2006

Status

approved