## triangle, row sums = Sigma(n)

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• 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
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
• ... 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
--- 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
/\ against HTML mail /\ against gratuitous bloodshed

[stolen with permission from Daniel B. Cristofani]

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