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Search: id:A075443
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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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+0
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; listen)
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OFFSET
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0,8
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COMMENT
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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
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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
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a[n_] := Sum[If[GCD[h, n]==1, Abs[h-PowerMod[h, -1, n]], 0], {h, 1, n}]/2
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CROSSREFS
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Cf. A075444-A075452.
Sequence in context: A127447 A096272 A021715 this_sequence A021250 A073758 A133995
Adjacent sequences: A075440 A075441 A075442 this_sequence A075444 A075445 A075446
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KEYWORD
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nonn
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AUTHOR
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Michele Dondi (bik.mido(AT)tiscalinet.it), Sep 18 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Sep 20 2002
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