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A160255 The sum of all the entries in an n x n Cayley table for multiplication in Z_n. 0
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

If n is prime, then A_n= (n-1)(n^2-n)/2.

Thanks to David Miller.

LINKS

Table of n, a(n) for n=1..44.

FORMULA

a(n)= Sigma(i=1 to n-1) (n*(gcd(n,i))/2)*((n/(gcd(n,i))-1).

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) = sum(i=1, n-1, (n*(gcd(n, i))/2)*((n/(gcd(n, i))-1))) \\ Michel Marcus, Jun 16 2013

CROSSREFS

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

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Last modified April 22 22:19 EDT 2021. Contains 343197 sequences. (Running on oeis4.)