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A075443
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a(n)=(1/2)Sum_h |h-h'| with h and h' in [1,n], gcd(h,n)=1, hh'=1 (mod n).
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10
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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; internal format)
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OFFSET
| 0,8
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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.
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LINKS
| 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.
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MATHEMATICA
| a[n_] := Sum[If[GCD[h, n]==1, Abs[h-PowerMod[h, -1, n]], 0], {h, 1, n}]/2
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CROSSREFS
| Cf. A075444-A075452.
Sequence in context: A127447 A096272 A021715 * A021250 A073758 A133995
Adjacent sequences: A075440 A075441 A075442 * A075444 A075445 A075446
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KEYWORD
| nonn
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AUTHOR
| Michele Dondi (bik.mido(AT)tiscalinet.it), Sep 18 2002
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Sep 20 2002
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