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triangle, row sums = Sigma(n)

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  • matrixmonitor
    1,2,1,3,0,1,4,2,0,1,5,0,0,0,1,6,3,2,0,0,1,7,0,0,0,0,0,1,8,4,0,2,0,0,0, %T A126988 1,9,0,3,0,0,0,0,0,1,10,5,0,0,2,0,0,0,0,1,11,0,0,0,0,0,0,0,0,0,1,12,6,4 , %U
    Message 1 of 2 , Jan 5, 2007
    • 0 Attachment
      1,2,1,3,0,1,4,2,0,1,5,0,0,0,1,6,3,2,0,0,1,7,0,0,0,0,0,1,8,4,0,2,0,0,0,
      %T A126988
      1,9,0,3,0,0,0,0,0,1,10,5,0,0,2,0,0,0,0,1,11,0,0,0,0,0,0,0,0,0,1,12,6,4
      ,
      %U A126988 3,0,2,0,0,0,0,0,0
      %N A126988 Triangle, row sums = Sigma(n).
      %C A126988 Row sums = A000203, (Sigma(n)): 1, 3, 4, 7, 6, 12, 8,
      15,... Sigma(n) is the sum of the divisors of the integer n.
      Conjecture: The sequence of parsed terms in Sigma(n) is the reversal
      of non-zero row terms in the triangle A126988.
      %D A126988 David Wells, "Prime Numbers, the Most Mysterious Figures
      in Math", John Wiley & Sons, Inc, 2005, Appendix B.
      %F A126988 Row sums of a triangle in which k-th column (k=0,1,2...)
      is (1,2,3,...) interspersed with n consecutive zeros, starting after
      the "1".
      %e A126988 First few rows of the triangle are:
      %e A126988 1;
      %e A126988 2, 1;
      %e A126988 3, 0, 1;
      %e A126988 4, 2, 0, 1;
      %e A126988 5, 0, 0, 0, 1;
      %e A126988 6, 3, 2, 0, 0, 1;
      %e A126988 7, 0, 0, 0, 0, 0, 1;
      %e A126988 8, 4, 0, 2, 0, 0, 0, 1;
      %e A126988 9, 0, 3, 0, 0, 0, 0, 0, 1;
      %e A126988 10, 5, 0, 0, 2, 0, 0, 0, 0, 1;
      %e A126988 ..
      %e A126988 Sigma(12) = 28 = (from tables): (1 + 2 + 3 + 4 + 6 + 12).
      %e A126988 Sigma(12) = 28, from 12-th row of A126988 = (12 + 6 + 4 +
      3 + 2 + 1), deleting the zeros, from left to right.
      %Y A126988 Cf. A000203.
      %K A126988 nonn,tabl,uned
      %O A126988 1,2
      %A A126988 Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 31 2006
    • Phil Carmody
      ... That much seems true. ... What the blazes are parsed terms? ... This sequence isn t the row sums of any triangle, it is a triangle. ... So,
      Message 2 of 2 , Jan 6, 2007
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        --- matrixmonitor <matrixmonitor@...> wrote:
        > 1,2,1,3,0,1,4,2,0,1,5,0,0,0,1,6,3,2,0,0,1,7,0,0,0,0,0,1,8,4,0,2,0,0,0,
        > %T A126988
        > 1,9,0,3,0,0,0,0,0,1,10,5,0,0,2,0,0,0,0,1,11,0,0,0,0,0,0,0,0,0,1,12,6,4
        > ,
        > %U A126988 3,0,2,0,0,0,0,0,0
        > %N A126988 Triangle, row sums = Sigma(n).

        That much seems true.

        > %C A126988 Row sums = A000203, (Sigma(n)): 1, 3, 4, 7, 6, 12, 8,
        > 15,... Sigma(n) is the sum of the divisors of the integer n.
        > Conjecture: The sequence of parsed terms in Sigma(n) is the reversal

        What the blazes are 'parsed' terms?

        > of non-zero row terms in the triangle A126988.
        > %D A126988 David Wells, "Prime Numbers, the Most Mysterious Figures
        > in Math", John Wiley & Sons, Inc, 2005, Appendix B.
        > %F A126988 Row sums of a triangle in which k-th column (k=0,1,2...)
        > is (1,2,3,...) interspersed with n consecutive zeros, starting after
        > the "1".

        This sequence isn't the row sums of any triangle, it is a triangle.

        The descriptions are garbled, just as would be expected from:

        > %A A126988 Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 31 2006

        So, matrixmonitor, I don't remember seeing you post before. You're not just
        another sock-puppet for that previous known spewer of
        /stuff-of-questionable-quality/ are you?

        Phil

        () ASCII ribbon campaign () Hopeless ribbon campaign
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