A123229 Triangle read by rows: T(n, m) = n - (n mod m).

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

Offset

1,2

Comments

An equivalent definition: Consider A000012 as a lower-left all-1's triangle, and build the matrix product by multiplication with A127093 from the right. That is, T(n,m) = Sum_{j=m..n} A000012(n,j)*A127093(j,m) = Sum_{j=m..n} A127093(j,m) = m*floor(n/m) = m*A010766(n,m). - Gary W. Adamson, Jan 05 2007

The number of parts k in the triangle is A000203(k) hence the sum of parts k is A064987(k). - Omar E. Pol, Jul 05 2014

Links

G. C. Greubel, Rows n=1..100 of triangle, flattened

Example

Triangle begins:
{1},
{2, 2},
{3, 2, 3},
{4, 4, 3, 4},
{5, 4, 3, 4, 5},
{6, 6, 6, 4, 5, 6},
{7, 6, 6, 4, 5, 6, 7},
{8, 8, 6, 8, 5, 6, 7, 8},
{9, 8, 9, 8, 5, 6, 7, 8, 9},
...

Maple

seq(seq(n-modp(n, m), m=1..n), n=1..13); # Muniru A Asiru, Oct 12 2018

Mathematica

a = Table[Table[n - Mod[n, m], {m, 1, n}], {n, 1, 20}]; Flatten[a]

Prog

(PARI) for(n=1, 9, for(m=1, n, print1(n-n%m", "))) \\ Charles R Greathouse IV, Nov 07 2011
(GAP) Flat(List([1..10], n->List([1..n], m->n-(n mod m)))); # Muniru A Asiru, Oct 12 2018

Crossrefs

Cf. A074025, A093960.

Cf. also A024916 (row sums), A127093, A127094, A127096, A127097, A127098, A127099, A038040, A000203, A126988, A127013, A127057.

Sequence in context: A322832 A348389 A073453 * A127095 A249871 A330408

Adjacent sequences: A123226 A123227 A123228 * A123230 A123231 A123232

Keyword

nonn,tabl,easy

Author

Roger L. Bagula and Gary W. Adamson, Oct 06 2006

Extensions

Edited by N. J. A. Sloane, Jul 05 2014 at the suggestion of Omar E. Pol, who observed that A127095 (Gary W. Adamson, with edits by R. J. Mathar) was the same as this sequence.

Status

approved