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A074639
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a(n)=Sum_h (hh'-1)/n with h and h' in [1,n], (h,n)=1, hh'=1 (mod n).
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10
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0, 0, 0, 1, 2, 5, 4, 11, 10, 15, 12, 31, 16, 39, 28, 36, 34, 75, 32, 91, 52, 64, 60, 145, 64, 115, 88, 141, 84, 225, 76, 241, 146, 160, 152, 250, 104, 319, 204, 272, 172, 419, 152, 447, 280, 286, 228, 599, 208, 501, 252, 440, 348, 727
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| For a given n a(n) is the sum for h ranging over the set of least nonnegative residues coprimes with n of (hh'-1)/n, where h' is the (unique) number in the same set such that hh'=1 (mod n).
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LINKS
| M. Dondi, Plot of A074639(n)/phi(n) (Euler's totient function) against the line y=x/4 in the range [0,100].
M. Dondi, Plot of A074639(n)/phi(n) (Euler's totient function) against the line y=x/4 in the range [0,1000].
M. Dondi, Plot of A074639(n)/phi(n) (Euler's totient function) against the line y=x/4 in the range [0,10000].
M. Dondi, Plot of A074639(n)/phi(n) (Euler's totient function) against the line y=x/4 in the range [0,10000] showing only one point out of every 5.
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EXAMPLE
| (1,n)=1 for all n, 1*1=1, so 1 contributes 0 to the sum. (n-1,n)=1 for all n, (n-1)^2=1 (mod n), so n-1 contributes n-2. Thus a(6)=4, in fact only 1 and 5 are coprime with 6 in {1,...,6}; a(5)=2*1+(5-2), in fact 2*3=6=1 (mod 5) and 6=5+1.
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CROSSREFS
| Cf. A074640-A074644.
Sequence in context: A069913 A072403 A010078 * A002314 A177979 A094471
Adjacent sequences: A074636 A074637 A074638 * A074640 A074641 A074642
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KEYWORD
| nonn
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AUTHOR
| Michele Dondi (bik.mido(AT)tiscalinet.it), Sep 12, 2002
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