The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A259748 a(n) = (Sum_{0
 0, 0, 2, 3, 0, 1, 0, 2, 6, 0, 0, 5, 0, 7, 10, 4, 0, 12, 0, 15, 14, 11, 0, 22, 0, 0, 18, 21, 0, 5, 0, 8, 22, 0, 0, 15, 0, 19, 26, 10, 0, 28, 0, 33, 30, 23, 0, 44, 0, 0, 34, 39, 0, 9, 0, 14, 38, 0, 0, 25, 0, 31, 42, 16, 0, 44, 0, 51, 46, 35, 0, 66, 0, 0, 50 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS {a(n)/n: n=1,2,...} = {0, 1/6, 1/4, 5/12, 1/2, 2/3, 3/4, 11/12}. From Danny Rorabaugh, Oct 22 2015: (Start) a(n)/n = 0 iff n mod 24 = 1,2,5,7,10,11,13,17,19,23 (A259749); a(n)/n = 1/6 iff n mod 24 = 6 (A259752); a(n)/n = 1/4 iff n mod 24 = 8,16 (A259751); a(n)/n = 5/12 iff n mod 24 = 12 (A073762); a(n)/n = 1/2 iff n mod 24 = 14,22 (A259750); a(n)/n = 2/3 iff n mod 24 = 3,9,15,18,21 (A259754); a(n)/n = 3/4 iff n mod 24 = 4,20 (A259755); a(n)/n = 11/12 iff n mod 24 = 0 (A008606). (End) LINKS Danny Rorabaugh, Table of n, a(n) for n = 1..24000 Danny Rorabaugh, Proof of a(n)/n values for A259748 FORMULA a(n) = A000914(n) mod n = (1/24)*(-1 + n)*n*(1 + n)*(2 + 3*n) mod n. a(24k) = 22k; a(24k+1) = 0; a(24k+2) = 0; a(24k+3) = 16k+2; a(24k+4) = 18k+3; a(24k+5) = 0; a(24k+6) = 4k+1, a(24k+7) = 0; a(24k+8) = 6k+2; a(24k+9) = 16k+6; a(24k+10) = 0; a(24k+11) = 0; a(24k+12) = 10k+5; a(24k+13) = 0; a(24k+14) = 12k+7; a(24k+15) = 16k+10; a(24k+16) = 6k+4; a(24k+17) = 0; a(24k+18) = 16k+12; a(24k+19) = 0; a(24k+20) = 18k+15; a(24k+21) = 16k+14; a(24k+22) = 12k+11; a(24k+23) = 0. - Danny Rorabaugh, Oct 22 2015 MATHEMATICA A[n_]:=Sum[a b, {a, 1, n}, {b, a+1, n}]; Table[Mod[A[n], n], {n, 1, 122}] PROG (PARI) vector(100, n, ((n-1)*n*(n+1)*(3*n+2)/24) % n) \\ Altug Alkan, Oct 22 2015 CROSSREFS Cf. A000914, A259749 (n such that a(n)=0), A259750 (n such that n/a(n)=2), A259751 (n such that n/a(n)=4), A259752 (n such that n/a(n)=6), A073762 (n such that n/a(n)=12/5), A259754 (n such that n/a(n)=3/2), A259755 (n such that n/a(n)=4/3), A008606 (n such that n/a(n)=12/11). Sequence in context: A215151 A305806 A064722 * A357728 A357681 A357720 Adjacent sequences: A259745 A259746 A259747 * A259749 A259750 A259751 KEYWORD nonn,easy AUTHOR José María Grau Ribas, Jul 04 2015 STATUS approved

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

Last modified May 25 17:00 EDT 2024. Contains 372804 sequences. (Running on oeis4.)