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Search: id:A053575
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| A053575 |
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a(n) is the odd part of Phi[n]: a[n]=A0000265(A000010[n]). |
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+0
1
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| 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 5, 1, 3, 3, 1, 1, 1, 3, 9, 1, 3, 5, 11, 1, 5, 3, 9, 3, 7, 1, 15, 1, 5, 1, 3, 3, 9, 9, 3, 1, 5, 3, 21, 5, 3, 11, 23, 1, 21, 5, 1, 3, 13, 9, 5, 3, 9, 7, 29, 1, 15, 15, 9, 1, 3, 5, 33, 1, 11, 3, 35, 3, 9, 9, 5, 9, 15, 3, 39, 1, 27, 5, 41, 3, 1, 21, 7, 5, 11, 3, 9, 11, 15, 23
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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This is not necessarily the square-free kernel. E.g. for n=19, Phi[19]=18 is divisible by 9, an odd square. Values at which this kernel is 1 correspond to A003401 (polygons constructible with ruler and compass)
Multiplicative with a(2^e) = 1, a(p^e) = p^{e-1}A000265(p-1). Christian G. Bower (bowerc(AT)usa.net) May 16, 2005.
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EXAMPLE
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n=70=2*5*7, Phi[70]=24=8*3, so the odd kernel of 70 a(70)=3
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MATHEMATICA
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f1[x_] :=x/(Part[Flatten[FactorInteger[x]], 1]^ Part[Flatten[FactorInteger[x]], 2]); ta=Table[0, {100}]; g[x_] :=(1-Mod[x, 2])*f1[x]+Mod[x, 2]*x; j=1; Do[Print[g[EulerPhi[n]]]; ta[[j]]=g[EulerPhi[n]]; j=j+1, {n, 2, 100}]; ta
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CROSSREFS
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Cf. A000010, A000265.
Sequence in context: A085417 A095660 A035648 this_sequence A103790 A013603 A157892
Adjacent sequences: A053572 A053573 A053574 this_sequence A053576 A053577 A053578
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KEYWORD
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nonn,mult
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jan 18 2000
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