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A036391
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a(n) = sum of order of a mod n, 0 < a < n, gcd(a, n) = 1.
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5
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0, 1, 3, 3, 11, 3, 21, 7, 21, 11, 63, 7, 77, 21, 23, 23, 171, 21, 183, 23, 49, 63, 333, 15, 231, 77, 183, 49, 473, 23, 441, 87, 147, 171, 161, 49, 671, 183, 161, 47, 903, 49, 903, 147, 161, 333, 1521, 47, 903, 231, 343, 161, 1727, 183, 483, 105, 427, 473, 2439, 47
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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Related to a problem of Arnold.
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LINKS
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FORMULA
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On the GRH, Kurlberg & Pomerance show that a(n) = n^2/log n exp(B log log n/log log log n (1 + o(1))), where B = A218342 = 0.345372.... - Charles R Greathouse IV, Oct 26 2012
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MAPLE
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with(numtheory):
a:= n-> add(`if`(igcd(n, k)=1, order(k, n), 0), k=1..n-1):
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MATHEMATICA
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a[n_] := Sum[ If[ CoprimeQ[k, n], MultiplicativeOrder[k, n], 0], {k, 1, n-1}]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Aug 19 2013 *)
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PROG
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(Haskell)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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