Search: id:A137818
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%I A137818
%S A137818 295569,1811079,1964375,2069469,4473387,5854375,10936053,13260625,
%T A137818 18029709,21576537,22182093,25536875,35595625,46404333,49648383,
%U A137818 55094375,57044817,58650625,67009923,69166467,72681875,76106875
%N A137818 Non-biquadratefree "year numbers": phi(n) = 2 phi(sigma(n)) and p^4 | 
               n for some p>1.
%C A137818 See A137815 for general comments and references about "year numbers". 
               This is the subsequence of elements of A137815 divisible by a biquadrateful 
               number, i.e. its intersection with A046101 (numbers divisible by 
               the 4th power of some prime). As such, it is of course also a subsequence 
               of A137817 and a fortiori of A137816.
%C A137818 There are only 28 such numbers below 10^8.
%o A137818 (PARI) for( i=1,#A137816, vecmax( factor( A137816[i])[,2])>3 && print1(A137816[i]", 
               "))
%o A137818 (PARI) for( i=1,#A046099, eulerphi(A046099[i])==2*eulerphi(sigma(A046099[i])) 
               && print1( A046099[i] ", "))
%o A137818 (PARI) for( n=1,10^9, issquarefree(n) && next; vecmax(factor(n)[,2])>
               3 || next; eulerphi(n)==2*eulerphi(sigma(n)) && print1(n", "))
%Y A137818 Cf. A137815-A137819, A046101.
%Y A137818 Sequence in context: A023351 A109031 A137817 this_sequence A164946 A048906 
               A119740
%Y A137818 Adjacent sequences: A137815 A137816 A137817 this_sequence A137819 A137820 
               A137821
%K A137818 nonn
%O A137818 1,1
%A A137818 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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