1,2

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. The sequence of parsed terms in sigma(n) is the reversal of non-zero row terms in the triangle A126988.

T(n,k)=n/k if k is a divisor of n; T(n,k)=0 if k is not a divisor of n (1<=k<=n). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 17 2007

The nonzero entries of row n are the divisors of n in decreasing order. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 17 2007

David Wells, "Prime Numbers, the Most Mysterious Figures in Math", John Wiley & Sons, Inc, 2005, Appendix B.

G.f. of column k = z^k/(1-z^k)^2 (k=1,2,...). G.f.=G(t,z)=Sum(t^k*z^k/(1-z^k)^2,k=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 17 2007

First few rows of the triangle are:

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, 1;

9, 0, 3, 0, 0, 0, 0, 0, 1;

10, 5, 0, 0, 2, 0, 0, 0, 0, 1;

...

sigma(12) = 28 = (from tables): (1 + 2 + 3 + 4 + 6 + 12).

sigma(12) = 28, from 12-th row of A126988 = (12 + 6 + 4 + 3 + 2 + 1), deleting the zeros, from left to right.

T:=proc(n, k) if type(n/k, integer)=true then n/k else 0 fi end: for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 17 2007

Cf. A000203.

Sequence in context: A120251 A071490 A127094 this_sequence A130026 A113287 A096798

Adjacent sequences: A126985 A126986 A126987 this_sequence A126989 A126990 A126991

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 31 2006

Edited by njas, Jan 24 2007