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A070818
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Smallest argument m such that Commutator[Phi(n),P(n)] = 2n-1, where Phi(n)=A000010(n) and P(n)=A006530, the largest prime factor of n.
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0
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45, 5, 7, 11, 143, 13, 23, 119, 17, 19, 667, 713, 29, 47, 31, 6929, 59, 407, 37, 41, 2867, 53, 83, 3149, 164561, 3233, 1403, 25631, 107, 61, 3763, 1633, 1679, 71, 79, 803, 73, 5959, 4559, 4717, 89, 4841, 36461, 167, 103, 5353, 179, 1067, 97, 101, 2507, 5989
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Only five (no more) even commutator-values appear at the arguments of known Fermat-primes. These are listed in A070813. Still 0 and -1 emerge: A070812[3]=0 and A070812[4]=-1.
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FORMULA
| a(n)=Min{x; Phi[P(x)]-P[Phi(x)]=2n-1= Min{x; A000010[A006530(x)]-A006530[A000010(x)]=2n-1}
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EXAMPLE
| f[m]=A070812(m)=A000010[A006530(m)]-A006530[A000010(m)] f[m]=1: appears first at m=45: Phi[45]=24,P(24)=3,P(45)=5,Phi(5)=4, so a(1)=Phi(5)-P(24)=4-3=1; Also a(255)=3321377=97.97.353: because its largest p factor P=353,Phi[353]=352,Phi[3321377]=3277824=1024.3.11.97, with max prime factor = 97. Thus a(255)=352-97=255.
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MATHEMATICA
| pf[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] f[x_] := EulerPhi[pf[n]]-pf[EulerPhi[n]] t=Table[0, {257}]; Do[s=f[n]; If[s<258&&t[[s]]==0, t[[s]]=n], {n, 3, 4000000}]; t
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CROSSREFS
| Cf. A070812, A000010, A006530, A070813, A000215.
Sequence in context: A131994 A037940 A037218 * A129536 A108909 A033365
Adjacent sequences: A070815 A070816 A070817 * A070819 A070820 A070821
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), May 10 2002
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