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A123229 Triangle read by rows: T(n, m) = n - (n mod m). 7
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A322832 A348389 A073453 * A127095 A249871 A330408
KEYWORD
nonn,tabl,easy
AUTHOR
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

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Last modified July 19 20:58 EDT 2024. Contains 374436 sequences. (Running on oeis4.)