Search: id:A058887
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%I A058887
%S A058887 7,17,19,19,19,31,31,47,47,47,47,47,47,47,47,47,47,47,47,47,47,47,47,
%T A058887 47,47,47,47,47,47,47,47,47,47,47,47,47,47,47,47,47,47,47,47,47,47,47,
%U A058887 47,47,47,47,47,47,47,47,47
%N A058887 Smallest prime such that invphi((2^n)*p) is an empty set, i.e.(2^n)*p 
               is a non-totient number.
%C A058887 First 0-s in sequences were searched for k=1..256:
%F A058887 Min{p|p is prime and nops(invphi((2^n)*p))=0}
%e A058887 For n=1, the initial segment of {2p} sequence is nops(invphi({2p}))={4, 
               4, 2, 0, 2, 0, 0, 0, 2, 2, ...}, where the position of the first 
               0 is 4, corresponding to p(4)=7, so a(4)=4. For n=8 the same initial 
               segment is: {11, 32, 23, 18, 24, 10, 11, 4, 9, 21, 2, 16, 9, 12, 
               0, 14, 5, 6, 12, ...}, where the first 0 is the 15th, corresponding 
               to p(15)=47, thus a(15)=47. nops(invphi(47*(2^n)))=0 holds for n=1, 
               ...1482, while inv(47*(2^1483) is not empty because 1+47*(2^1483) 
               is a large prime q and Phi(q)=Phi(2q)=47*2^1483. Thus after n=1482, 
               47 has to be replaced by some other prime. For p(k), k<15 the relevant 
               invphi sets are not empty. Do exist primes p at all, such that nops(invphi(p*2^n))=0 
               holds for all n or not?
%p A058887 [seq(nops(invphi(2^k*ithprime(i))),i=1..256)];
%Y A058887 A005277, A007617, A002020, A000010, A051953.
%Y A058887 Sequence in context: A071615 A067459 A101240 this_sequence A167797 A001913 
               A071845
%Y A058887 Adjacent sequences: A058884 A058885 A058886 this_sequence A058888 A058889 
               A058890
%K A058887 nonn
%O A058887 0,1
%A A058887 Labos E. (labos(AT)ana.sote.hu), Jan 08 2001

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