A130212 T(k, n) = sum_(1 <= j <= k) [j | k] j mu(k / j) floor(n / k), triangle read by rows.

1, 2, 1, 3, 1, 2, 4, 2, 2, 2, 5, 2, 2, 2, 4, 6, 3, 4, 2, 4, 2, 7, 3, 4, 2, 4, 2, 6, 8, 4, 4, 4, 4, 2, 6, 4, 9, 4, 6, 4, 4, 2, 6, 4, 6, 10, 5, 6, 4, 8, 2, 6, 4, 6, 4, 11, 5, 6, 4, 8, 2, 6, 4, 6, 4, 10, 12, 6, 8, 6, 8, 4, 6, 4, 6, 4, 10, 4, 13, 6, 8, 6, 8, 4, 6, 4, 6, 4, 10, 4, 12

Offset

1,2

Links

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

Formula

A000012 * A054522 as infinite lower triangular matrices (previous name).

T(n,n) = A000010(n).

Example

First few rows of the triangle are:
1;
2, 1;
3, 1, 2;
4, 2, 2, 2;
5, 2, 2, 2, 4;
6, 3, 4, 2, 4, 2;
7, 3, 4, 2, 4, 2, 6;
8, 4, 4, 4, 4, 2, 6, 4;
9, 4, 6, 4, 4, 2, 6, 4, 6;
10, 5, 6, 4, 8, 2, 6, 4, 6, 4;
...

Maple

with(numtheory): A130212 := (n, k) -> add(j*mobius(k / j)*iquo(n, k), j = divisors(k)); # Peter Luschny, Oct 28 2010

Mathematica

A[n_, k_] := Sum[j MoebiusMu[k/j] Floor[n/k], {j, Divisors[k]}];
Table[A[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 14 2019 *)

Crossrefs

Cf. A000010, A130211 (product with swapped matrices), A054522, A000217 (row sums).

Sequence in context: A056951 A130517 A316715 * A133737 A213361 A212121

Adjacent sequences: A130209 A130210 A130211 * A130213 A130214 A130215

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, May 17 2007

Extensions

Name replaced by new formula by Peter Luschny, Oct 28 2010

T(6,1) corrected by R. J. Mathar, Aug 06 2016

Status

approved