OFFSET
1,2
COMMENTS
The dot product of the n-th row of this triangle and the n-th row of triangle A259177 equals A024916(n), the sum of all divisors of numbers 1 through n (true for all n <= 20000); the value of a(n) is the sum of the rectangles between the y-axis and the vertical legs of the symmetric representation of sigma(n). This is the companion computation to A283368.
FORMULA
EXAMPLE
The first vertical leg of the symmetric representation of sigma(15) is at x-coordinate 8 and has length 3, and row 15 has 5 entries so that T(15,1) = 8 and T(15,5) = 15.
The first 16 rows of the irregular triangle:
1: 1
2: 2
3: 2 3
4: 3 4
5: 3 5
6: 4 5 6
7: 4 5 7
8: 5 6 8
9: 5 7 9
10: 6 7 8 10
11: 6 7 8 11
12: 7 9 10 12
13: 7 9 10 13
14: 8 9 11 14
15: 8 10 11 12 15
16: 9 11 12 13 16
MATHEMATICA
(* function f[n, k] and its support functions are defined in A237593 *)
a283367[n_, k_] := Sum[f[n, 2*i-1], {i, k}]
TableForm[Table[a283367[n, k], {n, 1, 16}, {k, 1, row[n]}]] (* triangle *)
Flatten[Table[a283367[n, k], {n, 1, 21}, {k, 1, row[n]}]] (* sequence data *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Hartmut F. W. Hoft, Mar 06 2017
STATUS
approved