Search: id:A070159
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%I A070159
%S A070159 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,
%T A070159 101,103,107,109,113,127,131,133,137,139,149,151,157,163,167,173,179,
%U A070159 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269
%N A070159 Numbers n such that phi[n]/(sigma[n]-n) is an integer.
%C A070159 This sequence consists of all primes p (for which the given ratio equals 
               (p-1)/1, see A000040) and of composites listed in A055940 (see examples).
%C A070159 Up to 10^7, there is no element of this sequence having more than 2 prime 
               factors. - M. F. Hasler, Dec 11 2007
%F A070159 { a(k) } = { n in N | A000010(n)/A001065(n) is an integer }.
%F A070159 { a(k) } = { A000040(k) } union { A055940(k) }.
%e A070159 The prime p=47 is in this sequence since phi[p]/(sigma[p]-p) = p-1 is 
               an integer, as is the case for any other prime.
%e A070159 The composite n=403=13*31 is in this sequence, since the ratio Phi[n]/
               (sigma[n]-n) =360/(1+13+31)=8 is an integer.
%e A070159 The first few composites in this sequence are 133,403,583,713,... (A055940)
%t A070159 Do[s=EulerPhi[n]/(DivisorSigma[1, n]-n); If[IntegerQ[s], Print[n]], {n, 
               2, 1000}]
%o A070159 (PARI) for(n=2,999,eulerphi(n)%(sigma(n)-n)|print1(n",")) \\ - M. F. 
               Hasler, Dec 11 2007
%Y A070159 Cf. A000010, A000040, A001065, A000203, A055940, A070037, A020492, A068418, 
               A062972.
%Y A070159 Sequence in context: A137589 A052424 A055398 this_sequence A158611 A000040 
               A008578
%Y A070159 Adjacent sequences: A070156 A070157 A070158 this_sequence A070160 A070161 
               A070162
%K A070159 nonn
%O A070159 1,1
%A A070159 Labos E. (labos(AT)ana.sote.hu), Apr 26 2002
%E A070159 Edited by M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Dec 11 2007

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