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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 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

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