OFFSET
1,1
COMMENTS
If S=(s(1),s(2),...) is a sequence written as a row vector, then S*T is the summatory sequence of S; i.e. its n-th term is Sum{s(k): k|n}. T is the transpose of the left summatory matrix, A077049; T is the inverse of the right Moebius transformation matrix. See A077049 for further properties.
This is essentially the same as A051731, which includes only the triangle. Note that the standard in the OEIS is left to right antidiagonals, which would make this the left summatory matrix, and A077049 the right one. - Franklin T. Adams-Watters, Apr 08 2009
Sum of column k is A000005. - Geoffrey Critzer, Mar 29 2015
FORMULA
T(n, k)=1 if n|k else T(n, k)=0.
From Boris Putievskiy, May 08 2013: (Start)
As table T(n,k)= floor(n/k)-floor((n-1)/k).
a(n) = floor(i/j) - floor((i-1)/j), where i=n-t*(t+1)/2, j=(t*t+3*t+4)/2-n, t=floor((-1+sqrt(8*n-7))/2). (End)
G.f. for row n: x^n/(1-x^n). - Geoffrey Critzer, Mar 29 2015
EXAMPLE
Northwest corner:
1 1 1 1 1 1
0 1 0 1 0 1
0 0 1 0 0 1
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
MATHEMATICA
(* returns the northwest corner *) nn = 20; Table[PadRight[Drop[CoefficientList[Series[x^n/(1 - x^n), {x, 0, nn}], x], 1], nn], {n, 1, nn}] // Grid (* Geoffrey Critzer, Mar 29 2015 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Oct 22 2002
STATUS
approved