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 A281376 Total number of counts where floor(N/k) < floor((N+k)/n) for k = {1, 2, ..., n-1} and N >= n. 1
 0, 0, 0, 1, 3, 6, 11, 17, 25, 35, 47, 60, 77, 95, 115, 138, 164, 191, 222, 254, 290, 329, 370, 412, 460, 510, 562, 617, 676, 736, 802, 869, 940, 1014, 1090, 1169, 1255, 1342, 1431, 1523, 1621, 1720, 1825, 1931, 2041, 2156, 2273, 2391, 2517, 2645, 2777 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (terms 1..200 from Lorenz H. Menke, Jr.) FORMULA a(n) = Sum_{d=1..ceiling((n-3)/3)} Sum_{j=1..n-(2*d+1)} floor(j/d). - Jon E. Schoenfield, Jan 23 2017 a(n) = Sum_{d=1..ceiling(n/3)-1} ((j+1)*(j*d/2 + n mod d)), where j = floor(n/d) - 3. - Jon E. Schoenfield, Jan 24 2017 EXAMPLE For n = 5, we have counted the cases where floor(N/k) < floor((N+k)/5), k = {1,2,3,4} then a(5) = 3, since this is true only for k = 4 and N = 6, k = 4 and N = 7, and k = 4 and N = 11. MAPLE A281376 := proc(n) local a, k, N; a := 0 ; for k from 1 to n-1 do for N from n do if floor(N/k) < floor((N+k)/n) then a := a +1 ; elif N >= (k+2*n)*k/(n-k) then break; end if; end do: end do: a ; end proc: seq(A281376(n), n=1..10) ; # R. J. Mathar, Feb 03 2017 MATHEMATICA a[n_] := Block[{lhs, rhs, count}, count = 0; Do[lhs = Floor[H1/k]; rhs = Floor[(H1 + k)/n]; If[lhs < rhs, count++], {k, 1, n - 1}, {H1, n, (n^2 - 3 n + 1) + 10}]; (* the 10 is simply guard counts *) Return[count]]; a281376[n_] := Sum[Floor[j/d], {d, Ceiling[(n - 3)/3]}, {j, n - (2 d + 1)}] (* Hartmut F. W. Hoft, Jan 25 2017; based on the first formula above *) PROG (PARI) a(n) = sum(d = 1, ceil((n-3)/3), sum(j = 1, n-(2*d+1), j\d)); \\ Michel Marcus, Jan 29 2017 CROSSREFS Sequence in context: A273140 A320272 A119639 * A247586 A107957 A000603 Adjacent sequences: A281373 A281374 A281375 * A281377 A281378 A281379 KEYWORD nonn AUTHOR Lorenz H. Menke, Jr., Jan 20 2017 STATUS approved

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Last modified December 6 09:20 EST 2022. Contains 358607 sequences. (Running on oeis4.)