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 A111490 Antidiagonal sums of the numerical array defined by M(n,k) = 1 + (k-1) mod n. 22
 1, 2, 4, 5, 9, 9, 15, 16, 21, 23, 33, 29, 41, 45, 51, 52, 68, 65, 83, 81, 91, 99, 121, 109, 128, 138, 152, 152, 180, 168, 198, 199, 217, 231, 253, 234, 270, 286, 308, 298, 338, 326, 368, 372, 384, 404, 450, 422, 463, 470, 500, 506, 558, 546, 584, 576, 610, 636 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Previous name was "Sum of the element of the antidiagonals of the numerical array M(m,n) defined as follows. First row (M11, M12, ..., M1n): 1, 1, 1, 1, 1, 1, ... (all 1's). Second row (M21, M22, ..., M2n): 1, 2, 1, 2, 1, 2, ... (sequence 1, 2 repeated). Third row (M31, M32, ..., M3n): 1, 2, 3, 1, 2, 3, 1, 2, 3, ... (sequence 1, 2, 3 repeated). Fourth row (M41, M42, ..., M4n): 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, ... (sequence 1, 2, 3, 4 repeated). And so on." Then the sequence is M(1,1), M(1,2) + M(2,1), M(1,3) + M(2,2) + M(3,1), etc., a(n) = Sum_{i=1..n} M(i, n-i+1). The successive determinants of the arrays are the factorial numbers (A000142). - Robert G. Wilson v LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = n + A004125(n). - Juri-Stepan Gerasimov, Aug 30 2009 a(n) = Sum_{i=1..n+1} (n mod i). - Wesley Ivan Hurt, Dec 05 2014 G.f.: 2*x/(1-x)^3 - (1-x)^(-1)*Sum_{k>=1} k*x^k/(1-x^k). - Robert Israel, Oct 11 2015 EXAMPLE Considering the 6 X 6 array: 1, 1, 1, 1, 1, 1 1, 2, 1, 2, 1, 2 1, 2, 3, 1, 2, 3 1, 2, 3, 4, 1, 2 1, 2, 3, 4, 5, 1 1, 2, 3, 4, 5, 6 The third element of the sequence is 1+2+1=4. The fifth element of the sequence is 1+2+3+2+1=9. MAPLE A111490:=n->add(n mod i, i=1..n+1): seq(A111490(n), n=1..100); # Wesley Ivan Hurt, Dec 05 2014 MATHEMATICA t = Table[Flatten@Table[Range@n, {m, Ceiling[99/n]}], {n, 99}]; f[n_] := Sum[ t[[i, n - i + 1]], {i, n}]; Array[f, 58] (* Robert G. Wilson v, Nov 22 2005 *) (* to view table *) Table[Flatten@Table[Range@n, {m, Ceiling[40/n]}], {n, 10}] // TableForm PROG (PARI) vector(100, n, n + sum(k=2, n, n % k)) \\ Altug Alkan, Oct 12 2015 (PARI) a(n) = sum(k=1, n, 2*k-sigma(k)); \\ Michel Marcus, Oct 11 2015 CROSSREFS Cf. A000142, A004125. Partial sums of A033879. - Gionata Neri, Sep 10 2015 Sequence in context: A167511 A242398 A174112 * A079784 A189210 A188969 Adjacent sequences:  A111487 A111488 A111489 * A111491 A111492 A111493 KEYWORD nonn,easy AUTHOR Paolo P. Lava and Giorgio Balzarotti, Nov 21 2005 EXTENSIONS Edited and extended by Robert G. Wilson v, Nov 22 2005 Name changed by Michel Marcus, Sep 23 2013 STATUS approved

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Last modified October 22 08:00 EDT 2019. Contains 328315 sequences. (Running on oeis4.)