Search: id:A137817
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%I A137817
%S A137817 295569,295947,1586763,1811079,1964375,2069469,4473387,5854375,6820555,
%T A137817 7285923,10936053,12233457,13260625,18029709,18052767,21153663,21576537,
%U A137817 21604131,22182093,22877451,23744043,25536875,28340307,34102775
%N A137817 Cubeful "year numbers" (such that phi(n) = 2 phi(sigma(n)): A137815).
%C A137817 See A137815 for general comments and references about "year numbers". 
               This is the subsequence of cubeful elements of A137815, i.e. its 
               intersection with A046099. As such, it is of course also a subsequence 
               of A137816.
%C A137817 There are only 56 such numbers below 10^8.
%H A137817 M. F. Hasler, <a href="b137817.txt">Table of n, a(n) for n=1,...,56</
               a>.
%o A137817 (PARI) for( i=1,#A137816, vecmax( factor( A137816[i] )[,2])>2 && print1(A137816[i]", 
               "))
%o A137817 (PARI) for( i=1,#A046099, eulerphi(A046099[i])==2*eulerphi(sigma(A046099[i])) 
               && print1( A046099[i] ", "))
%o A137817 (PARI) for( n=1,10^9, issquarefree(n) && next; vecmax(factor(n)[,2])>
               2 || next; eulerphi(n)==2*eulerphi(sigma(n)) && print1(n", "))
%Y A137817 Cf. A137815-A137819, A006872. A046099. A067704.
%Y A137817 Sequence in context: A050249 A023351 A109031 this_sequence A137818 A164946 
               A048906
%Y A137817 Adjacent sequences: A137814 A137815 A137816 this_sequence A137818 A137819 
               A137820
%K A137817 nonn
%O A137817 1,1
%A A137817 Richard K. Guy (rkg(AT)cpsc.ucalgary.ca), Richard J. Mathar (mathar(AT)strw.leidenuniv.nl) 
               and M. F. Hasler (MHasler(AT)univ-ag.fr), Feb 11 2008

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