Search: id:A070818
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%I A070818
%S A070818 45,5,7,11,143,13,23,119,17,19,667,713,29,47,31,6929,59,407,37,41,2867,
%T A070818 53,83,3149,164561,3233,1403,25631,107,61,3763,1633,1679,71,79,803,73,
%U A070818 5959,4559,4717,89,4841,36461,167,103,5353,179,1067,97,101,2507,5989
%N A070818 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.
%C A070818 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.
%F A070818 a(n)=Min{x; Phi[P(x)]-P[Phi(x)]=2n-1= Min{x; A000010[A006530(x)]-A006530[A000010(x)]=2n-1}
%e A070818 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.
%t A070818 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
%Y A070818 Cf. A070812, A000010, A006530, A070813, A000215.
%Y A070818 Sequence in context: A131994 A037940 A037218 this_sequence A129536 A108909 
               A033365
%Y A070818 Adjacent sequences: A070815 A070816 A070817 this_sequence A070819 A070820 
               A070821
%K A070818 nonn
%O A070818 1,1
%A A070818 Labos E. (labos(AT)ana.sote.hu), May 10 2002

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