|
|
A075443
|
|
a(n)=(1/2)Sum_h |h-h'| with h and h' in [1,n], gcd(h,n)=1, hh'=1 (mod n).
|
|
10
|
|
|
0, 0, 0, 0, 0, 1, 0, 4, 0, 6, 4, 10, 0, 25, 4, 12, 16, 33, 12, 46, 8, 42, 32, 58, 0, 101, 44, 60, 56, 97, 12, 130, 64, 126, 72, 98, 72, 247, 80, 108, 80, 243, 48, 310, 64, 162, 196, 312, 96, 354, 172, 228, 168, 417, 120, 302, 176, 378, 284, 444, 120, 729, 188, 294, 352
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,8
|
|
COMMENTS
|
For a given n, a(n) is half the sum for h ranging over the set of least positive residues coprime with n of |h-h'|, where h' is the (unique) number in the same set such that hh'=1 (mod n).
If h and h' are chosen randomly from [1,n] then the expected value of |h-h'|/2 is n/6. So it is plausible that a(n) ~ n*phi(n)/6 and numerical evidence seems to support that.
|
|
LINKS
|
|
|
MATHEMATICA
|
a[n_] := Sum[If[GCD[h, n]==1, Abs[h-PowerMod[h, -1, n]], 0], {h, 1, n}]/2
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Michele Dondi (bik.mido(AT)tiscalinet.it), Sep 18 2002
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|