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%I #11 Sep 01 2016 06:57:23
%S 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,
%T 60,56,97,12,130,64,126,72,98,72,247,80,108,80,243,48,310,64,162,196,
%U 312,96,354,172,228,168,417,120,302,176,378,284,444,120,729,188,294,352
%N a(n)=(1/2)Sum_h |h-h'| with h and h' in [1,n], gcd(h,n)=1, hh'=1 (mod n).
%C 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).
%C 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.
%H Ivan Neretin, <a href="/A075443/b075443.txt">Table of n, a(n) for n = 0..10000</a>
%H M. Dondi, <a href="/A075443/a075443_a.png">Plot of A075443(n)/phi(n) (Euler's totient function)</a> against the line y=x/6 in the range [0,100].
%H M. Dondi, <a href="/A075443/a075443_b.png">Plot of A075443(n)/phi(n) (Euler's totient function)</a> against the line y=x/6 in the range [0,1000].
%H M. Dondi, <a href="/A075443/a075443_c.png">Plot of A075443(n)/phi(n) (Euler's totient function)</a> against the line y=x/6 in the range [0,10000].
%H M. Dondi, <a href="/A075443/a075443_d.png">Plot of A075443(n)/phi(n) (Euler's totient function)</a> against the line y=x/6 in the range [0,10000] showing only one point out of every 5.
%t a[n_] := Sum[If[GCD[h, n]==1, Abs[h-PowerMod[h, -1, n]], 0], {h, 1, n}]/2
%Y Cf. A075444-A075452.
%K nonn
%O 0,8
%A Michele Dondi (bik.mido(AT)tiscalinet.it), Sep 18 2002
%E Edited by _Dean Hickerson_, Sep 20 2002
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