A134545 Triangle read by rows: T(n,k) = Sum_{i=k..n} (i+1-k)*A051731(n,i).

1, 3, 1, 4, 2, 1, 7, 4, 2, 1, 6, 4, 3, 2, 1, 12, 8, 5, 3, 2, 1, 8, 6, 5, 4, 3, 2, 1, 15, 11, 8, 6, 4, 3, 2, 1, 13, 10, 8, 6, 5, 4, 3, 2, 1, 18, 14, 11, 9, 7, 5, 4, 3, 2, 1, 12, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 22, 17, 13, 10, 8, 6, 5, 4, 3, 2, 1, 14, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)

Formula

Equals A051731 * A004736 as infinite lower triangular matrices.

From Andrew Howroyd, Sep 20 2025: (Start)

T(n,k) = Sum_{i=k..n} A135539(n,i).

T(n,k) = Sum_{d|n, d>=k} (d + 1 - k).

T(n,k) = A134559(n,k) - (k-1)*A135539(n,k). (End)

Example

First few rows of the triangle:
   1;
   3,  1;
   4,  2, 1;
   7,  4, 2, 1;
   6,  4, 3, 2, 1;
  12,  8, 5, 3, 2, 1;
   8,  6, 5, 4, 3, 2, 1;
  15, 11, 8, 6, 4, 3, 2, 1;
  ...

Prog

(PARI) T(n, k) = sumdiv(n, d, if(d>=k, d+1-k)) \\ Andrew Howroyd, Sep 20 2025

Crossrefs

Row sums are A007437.

Column 1 is A000203.

Cf. A051731, A004736, A134559, A135539.

Sequence in context: A135821 A289205 A283866 * A174907 A237016 A135822

Adjacent sequences: A134542 A134543 A134544 * A134546 A134547 A134548

Keyword

nonn,tabl

Author

Gary W. Adamson, Oct 31 2007

Extensions

New name and a(56) onwards from Andrew Howroyd, Sep 20 2025

Status

approved