

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
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OFFSET

1,2


COMMENTS

An equivalent definition: Consider A000012 as a lowerleft all1'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


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(nmodp(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

(GAP) Flat(List([1..10], n>List([1..n], m>n(n mod m)))); # Muniru A Asiru, Oct 12 2018


CROSSREFS

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


KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



