A134867 - OEIS

A134867

A010766 * A000012.

1, 3, 1, 5, 2, 1, 8, 4, 2, 1, 10, 5, 3, 2, 1, 14, 8, 5, 3, 2, 1, 16, 9, 6, 4, 3, 2, 1, 20, 12, 8, 6, 4, 3, 2, 1, 23, 14, 10, 7, 5, 4, 3, 2, 1, 27, 17, 12, 9, 7, 5, 4, 3, 2, 1, 29, 18, 13, 10, 8, 6, 5, 4, 3, 2, 1, 35, 23, 17, 13, 10, 8, 6, 5, 4, 3, 2, 1, 37, 24, 18, 14, 11, 9, 7, 6, 5, 4, 3, 2, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..91.

FORMULA

A010766 * A000012 as infinite lower triangular matrices.

Triangle read by rows, partial row sums of A010766 starting fromt the right.

G.f. of column k: 1/(1-x) * Sum_{j>=1} x^(k*j)/(1-x^j) = 1/(1-x) * Sum_{j>=k} x^j/(1-x^j). - Seiichi Manyama, Oct 30 2023

EXAMPLE

First few rows of the triangle:

3, 1;

5, 2, 1;

8, 4, 2, 1;

10, 5, 3, 2, 1;

14, 8, 5, 3, 2, 1;

16, 9, 6, 4, 3, 2, 1;

20, 12, 8, 6, 4, 3, 2, 1;

23, 14, 10, 7, 5, 4, 3, 2, 1;

27, 17, 12, 9, 7, 5, 4, 3, 2, 1;

...

MATHEMATICA

t = Table[Sum[Floor[n/h], {h, k, n}], {n, 0, 10}, {k, 1, n}];

u = Flatten[t] (* A134867 array *)

TableForm[t] (* A134867 sequence *)

(* Clark Kimberling, Oct 11 2014 *)

PROG

(PARI) T(n, k) = sum(j=k, n, n\j); \\ Seiichi Manyama, Oct 30 2023

CROSSREFS

Column k=1..4 give: A006218, A002541, A366968, A366972.

Row sums give A024916.

Cf. A010766, A135539.

Sequence in context: A100898 A101350 A199478 * A102573 A233940 A134033

Adjacent sequences: A134864 A134865 A134866 * A134868 A134869 A134870

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Nov 14 2007

EXTENSIONS

More terms from Seiichi Manyama, Oct 30 2023

STATUS

approved