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
KEYWORD
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