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Search: id:A083546
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| A083546 |
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Geometric mean of Euler-phi of 2 consecutive integers {n,n+1} is also an integer: these integer geometric mean values, sqrt(phi[n].phi[n+1]) are here. |
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3
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| 1, 2, 8, 12, 48, 48, 60, 80, 96, 128, 144, 180, 280, 240, 240, 288, 288, 288, 336, 288, 384, 360, 480, 480, 640, 720, 672, 600, 576, 720, 720, 720, 672, 864, 960, 864, 960, 1080, 1008, 1408, 1296, 960, 1008, 1320, 1260, 1056, 1440, 1200, 1728, 1440, 1296
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OFFSET
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1,2
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FORMULA
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a(m)=Sqrt(A000010[x]*A000010[x+1]) is integer. Sqrt(phi[x+1].phi[x])=Sqrt(A083542[x]) integer roots are given here.
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EXAMPLE
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x=19: phi[19]=18,phi[20]=8, 8.18=144-12.12, so 12 is here.
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MATHEMATICA
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f[x_] := EulerPhi[x]; Do[s=Sqrt[f[n+1]*f[n]]; If[IntegerQ[s], Print[s]], {n, 1, 5000}]
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CROSSREFS
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Cf. A000010, A083542, A083542, A066813, A058515, A083542-A083545.
Sequence in context: A135443 A143231 A104039 this_sequence A013190 A126192 A066471
Adjacent sequences: A083543 A083544 A083545 this_sequence A083547 A083548 A083549
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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), May 21 2003
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