The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 25 08:59 EST 2021. Contains 340416 sequences. (Running on oeis4.)