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%I #9 Mar 28 2014 02:28:56
%S 295569,1811079,1964375,2069469,4473387,5854375,10936053,13260625,
%T 18029709,21576537,22182093,25536875,35595625,46404333,49648383,
%U 55094375,57044817,58650625,67009923,69166467,72681875,76106875
%N Non-biquadratefree "year numbers": phi(n) = 2 phi(sigma(n)) and p^4 | n for some p>1.
%C 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 There are only 28 such numbers below 10^8.
%H Donovan Johnson, <a href="/A137818/b137818.txt">Table of n, a(n) for n = 1..500</a>
%o (PARI) for( i=1,#A137816, vecmax( factor( A137816[i])[,2])>3 && print1(A137816[i]", "))
%o (PARI) for( i=1,#A046099, eulerphi(A046099[i])==2*eulerphi(sigma(A046099[i])) && print1( A046099[i] ", "))
%o (PARI) for( n=1,10^9, issquarefree(n) && next; vecmax(factor(n)[,2])>3 || next; eulerphi(n)==2*eulerphi(sigma(n)) && print1(n", "))
%Y Cf. A137815-A137819, A046101.
%K nonn
%O 1,1
%A _R. K. Guy_, _R. J. Mathar_ and _M. F. Hasler_, Feb 11 2008