A122414 -id:A122414 - cp's OEIS frontend

A143535 Triangle read by rows, A122414 * A000012; 1<=k<=n.

0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 2, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Gary W. Adamson, Aug 23 2008

Row sums = A008472, the sum of distinct primes dividing n: (0, 2, 3, 2, 5, 5, 7, 2, 3, 7,...). Example: a(10) = 7 = 2 + 5.

			First few rows of the triangle =
0;
1, 1;
1, 1, 1;
1, 1, 0, 0;
1, 1, 1, 1, 1;
2, 2, 1, 0, 0, 0;
1, 1, 1, 1, 1, 1, 1;
1, 1, 0, 0, 0, 0, 0, 0;
1, 1, 1, 0, 0, 0, 0, 0, 0;
2, 2, 1, 1, 1, 0, 0, 0, 0, 0;
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
...
Example: row 6 = (2, 2, 1, 0, 0, 0) = partial sums starting from the right of row 6, A122414: (0, 1, 1, 0, 0, 0).

Cf. A122414, A008472.

Triangle read by rows, A122414 * A000012; 1<=k<=n. By rows, partial sums of A122414 terms starting from the right.

A122415 Triangle T(n,k) for 1 < k < n read by rows, where T(n,k) = 1 if gcd(n,k) is prime, 0 otherwise.

Original entry on oeis.org

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

Offset: 3

Klaus Brockhaus, Sep 03 2006

Triangle defined in A122414 without first column and main diagonal.

Cf. A122414.

Row sums are in A087625. [From Klaus Brockhaus, May 29 2009]

{m=14; v=vector(m,x,vector(x)); for(n=1,m,for(k=1,n-1,if(isprime(gcd(n+2,k+1)),v[n][k]=1))); for(n=1,m,for(k=1,n,print1(v[n][k],",")))}

cp's OEIS Frontend

A143535 Triangle read by rows, A122414 * A000012; 1<=k<=n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula