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Search: id:A072451
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| A072451 |
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Number of odd terms in the reduced residue system of 2n-1. |
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+0
5
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| 1, 1, 2, 3, 3, 5, 6, 4, 8, 9, 6, 11, 10, 9, 14, 15, 10, 12, 18, 12, 20, 21, 12, 23, 21, 16, 26, 20, 18, 29, 30, 18, 24, 33, 22, 35, 36, 20, 30, 39, 27, 41, 32, 28, 44, 36, 30, 36, 48, 30, 50, 51, 24, 53, 54, 36, 56, 44, 36, 48, 55, 40, 50, 63, 42, 65, 54, 36, 68, 69, 46, 60, 56
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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a(1)=1 and for n>1 a(n)=Phi(2n-1)/2 - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 11 2002
It would appear that a(n)=sum{k=0..n, abs(Jacobi(k, 2n-2k+1))}. - Paul Barry (pbarry(AT)wit.ie), Jul 20 2005
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EXAMPLE
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n=105: Phi[105]=48 with 24 odd, 24 even; for even n=2k reduced residue system consists only of odd terms, so number of odd terms equals Phi[n].
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MATHEMATICA
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gw[x_] := Table[GCD[x, w], {w, 1, x}] rrs[x_] := Flatten[Position[gw[x], 1]] Table[Count[OddQ[rrs[2*w-1]], True], {w, 1, 128}]
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CROSSREFS
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Cf. A000010, A037225.
Adjacent sequences: A072448 A072449 A072450 this_sequence A072452 A072453 A072454
Sequence in context: A046530 A003558 A141419 this_sequence A023156 A051599 A064464
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 19 2002
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