%I A057564
%S A057564 666,19674,309114,369594,715194,1180026,1924794,2722266,2741274,
%T A057564 4261914,5564826,6296634,6623226,6826266,7206906,9726648,15956154,
%U A057564 16046874,16478874,19263546,25333146,27706554,28151514,32938074
%N A057564 Natural numbers n for which the following three properties hold: (i) 
               Phi[Sigma[n]]=2*Phi[n], (ii) Sigma[n-2]=2*Sigma[Phi[n-2]], (iii) 
               Sigma[n+2]=2*Sigma[Phi[n+2]].
%C A057564 Called "Beastly neighbors" because 666 is the least element of the sequence 
               and because these numbers are seen to have a symmetric relationship 
               with their two "neighbors," using analogy to numbering houses on 
               the same side of the street (e.g. 664 and 668 are "neighbors" of 
               666).
%D A057564 D. Iannucci, "The neighbors of the Beast," Journal of Recreational Mathematics, 
               Volume 31, Number 1, 2002, pp. 52-55.
%e A057564 Phi[Sigma[666]]=Phi[1482]=432=2*216=2*Phi[666], Sigma[664]=1260=2*630=2*Sigma[328]=Sigma[Phi[664]], 
               Sigma[668]=1176=2*588=2*Sigma[332]=Sigma[Phi[668]]. Thus 666 is an 
               element of the sequence.
%Y A057564 Sequence in context: A043515 A051003 A104181 this_sequence A046694 A138563 
               A092797
%Y A057564 Adjacent sequences: A057561 A057562 A057563 this_sequence A057565 A057566 
               A057567
%K A057564 easy,nonn
%O A057564 1,1
%A A057564 Douglas E. Iannucci (diannuc(AT)uvi.edu), Oct 04 2000