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 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 Ivan Neretin, Table of n, a(n) for n = 0..10000 M. Dondi, Plot of A075443(n)/phi(n) (Euler's totient function) against the line y=x/6 in the range [0,100]. M. Dondi, Plot of A075443(n)/phi(n) (Euler's totient function) against the line y=x/6 in the range [0,1000]. M. Dondi, Plot of A075443(n)/phi(n) (Euler's totient function) against the line y=x/6 in the range [0,10000]. M. Dondi, Plot of A075443(n)/phi(n) (Euler's totient function) against the line y=x/6 in the range [0,10000] showing only one point out of every 5. MATHEMATICA a[n_] := Sum[If[GCD[h, n]==1, Abs[h-PowerMod[h, -1, n]], 0], {h, 1, n}]/2 CROSSREFS Cf. A075444-A075452. Sequence in context: A327278 A278210 A291540 * A021250 A073758 A133995 Adjacent sequences:  A075440 A075441 A075442 * A075444 A075445 A075446 KEYWORD nonn AUTHOR Michele Dondi (bik.mido(AT)tiscalinet.it), Sep 18 2002 EXTENSIONS Edited by Dean Hickerson, Sep 20 2002 STATUS approved

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Last modified September 20 16:31 EDT 2020. Contains 337265 sequences. (Running on oeis4.)