The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A160255 The sum of all the entries in an n X n Cayley table for multiplication in Z_n. 2
 0, 1, 6, 16, 40, 63, 126, 176, 270, 365, 550, 624, 936, 1099, 1350, 1664, 2176, 2349, 3078, 3280, 3948, 4631, 5566, 5712, 7000, 7813, 8748, 9520, 11368, 11475, 13950, 14592, 16236, 17969, 19390, 20304, 23976, 25327, 27222, 28400, 32800, 32949, 37926, 38896 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Thanks to David Miller. LINKS FORMULA a(p) = (p-1)*(p^2-p)/2, for p prime. a(n) = (n/2)*Sum_{i=1..n-1} gcd(n,i)*(n/gcd(n,i)-1). [Edited by Richard L. Ollerton, May 06 2021] a(n) = (n^2/2)*Sum_{d|n} phi(d)*(d-1)/d, where phi = A000010. - Richard L. Ollerton, May 06 2021 From Ridouane Oudra, Aug 24 2022: (Start) a(n) = Sum_{i=1..n} Sum_{j=1..n} (i*j mod n); a(n) = n^3/2 - (n/2)*Sum_{i=1..n} gcd(n,i); a(n) = n^3/2 - (n/2)*Sum_{d|n} d*tau(d)*moebius(n/d); a(n) = (A000578(n) - n*A018804(n))/2. (End) EXAMPLE For n=4: | 0 1 2 3 -+-------- 0| 0 0 0 0 1| 0 1 2 3 2| 0 2 0 2 3| 0 3 2 1 Sum becomes 6+4+6 = 16. PROG (PARI) a(n) = (n/2)*sum(i=1, n-1, gcd(n, i)*(n/gcd(n, i)-1)); \\ Michel Marcus, Jun 16 2013 [edited by Richard L. Ollerton, May 06 2021] CROSSREFS Cf. A000010, A000578, A018804. Sequence in context: A130902 A300371 A009955 * A213667 A123205 A123607 Adjacent sequences: A160252 A160253 A160254 * A160256 A160257 A160258 KEYWORD nonn AUTHOR David Byrne (david.roggeveen.byrne(AT)gmail.com), May 06 2009 EXTENSIONS More terms from Carl Najafi, Sep 29 2011 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 December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)