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Search: id:A070002
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| A070002 |
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Phi[P[n]]-P[Phi[n]] = 1, where P[x]=largest prime factor of x. |
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+0
7
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| 45, 90, 135, 175, 180, 270, 350, 360, 405, 525, 540, 700, 720, 810, 875, 1050, 1080, 1215, 1400, 1440, 1573, 1575, 1620, 1750, 2100, 2160, 2430, 2625, 2800, 2880, 3146, 3150, 3240, 3500, 3645, 4200, 4320, 4375, 4719, 4725, 4860, 5250, 5491, 5600, 5760
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OFFSET
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1,1
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COMMENT
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Phi[P[n]]-P[Phi[n]]=A000010[A006530(n)]- A006530[A000010(n)]=1, where P[x]=largest prime factor of x. Value of commutator of Phi and P functions at n equals -1.
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EXAMPLE
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m=77077=7.7.11.11.13.13 is here because P[m]=13,Ph[P(13)]=12 Phi[m]=55440=2.2.2.2.3.3.5.7.11 with P(Phi[55440])=13 and the difference is 13-12=1. Large part of but not all terms are divisible with 5.
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MATHEMATICA
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Do[s=EulerPhi[pf[n]]-pf[EulerPhi[n]]; If[Equal[s, 1], Print[n]], {n, 3, 100000}]
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CROSSREFS
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Cf. A000010, A006530, A068211, A070777, A070812, A070003, A070004, A007283, A070813-A070816.
Sequence in context: A043964 A140380 A115827 this_sequence A101794 A124017 A121925
Adjacent sequences: A069999 A070000 A070001 this_sequence A070003 A070004 A070005
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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 07 2002
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