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New triangle, row sums = primes

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  • matrixmonitor
    It s A130071 at EIS, http://www.tinyurl.com/4zq4q %I A130071 %S A130071 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 , %T A130071
    Message 1 of 1 , May 8, 2007
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      It's A130071 at EIS,
      http://www.tinyurl.com/4zq4q

      %I A130071
      %S A130071
      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
      ,
      %T A130071 12,2,0,3,0,0,0,0,0,18,2,1,0,0,9,0,0,0,0,17
      %N A130071 Triangle, A007444(k) in each column interspersed with k
      zeros.
      %C A130071 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.
      %F A130071 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.
      %e A130071 First few rows of the triangle are:
      %e A130071 2;
      %e A130071 2, 1;
      %e A130071 2, 0, 3;
      %e A130071 2, 1, 0, 4;
      %e A130071 2, 0, 0, 0, 9;
      %e A130071 2, 1, 3, 0, 0, 7;
      %e A130071 2, 0, 0, 0, 0, 0, 15;
      %e A130071 2, 1, 0, 4, 0, 0, 0, 12;
      %e A130071 2, 0, 3, 0, 0, 0, 0, 0, 18;
      %e A130071 2, 1, 0, 0, 9, 0, 0, 0, 0, 17;
      %e A130071 ..
      %Y A130071 Cf. A130070, A007444, A054525, A000040.
      %K A130071 nonn,tabl,new
      %O A130071 1,1
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