A130071 Triangle, A007444(k) in each column interspersed with k zeros.

2, 2, 1, 2, 0, 3, 2, 1, 0, 4, 2, 0, 0, 0, 9, 2, 1, 3, 0, 0, 7, 2, 0, 0, 0, 0, 0, 15, 2, 1, 0, 4, 0, 0, 0, 12, 2, 0, 3, 0, 0, 0, 0, 0, 18, 2, 1, 0, 0, 9, 0, 0, 0, 0, 17

Offset: 1

Author

Gary W. Adamson, May 05 2007

Keywords

• nonn
• tabl

Comments

Row sums = the primes. T(n,k) = 0 if k does not divide n. If k divides n, extract A007444(k) which become the nonzero terms of row n, sum = n-th prime. Example: The factors of 6 are (1, 2, 3 and 6) = k's for A007444(k) = (2 + 1 + 3 + 7) = p(6) = 13. A007444 = the Moebius transform of the primes, (2, 1, 3, 4, 9, 7, 15, 12, ...), as the right diagonal of A130071.

Examples

			First few rows of the triangle:
  2;
  2,  1;
  2,  0,  3;
  2,  1,  0,  4;
  2,  0,  0,  0,  9;
  2,  1,  3,  0,  0,  7;
  2,  0,  0,  0,  0,  0, 15;
  2,  1,  0,  4,  0,  0,  0, 12;
  2,  0,  3,  0,  0,  0,  0,  0, 18;
  2,  1,  0,  0,  9,  0,  0,  0,  0, 17;
  ...
		

Crossrefs

Cf. A130070, A007444, A054525, A000040.

Formula

Given the Moebius transform of the primes, A007444: (2, 1, 3, 4, 9, 7, 15, ...), the k-th term (k= 1,2,3,...) of this sequence generates the k-th column of A130071, interspersed with (k-1) zeros.