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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.
3
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
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
KEYWORD
nonn,tabl,easy
AUTHOR
Klaus Brockhaus, Sep 03 2006
STATUS
approved