%I A089189
%S A089189 2,3,5,7,11,13,17,19,23,29,31,37,43,47,53,59,61,67,71,79,83,97,101,103,
%T A089189 107,113,127,131,139,149,151,157,163,167,173,179,181,191,193,197,199,
%U A089189 211,223,227,229,239,241,257,263,269,277,283,293,307,311,317,331,337
%N A089189 Primes p such that p-1 is cube- or higher power-free.
%C A089189 The ratio of the count of primes p <= n such that p-1 is cube-free to 
               the count of primes <= n converges to 0.69.. . This implies that 
               roughly 70% of the primes less one are cube-free. This compares to 
               about 0.37 of the primes less one are square-free.
%e A089189 43 is included because 43-1 = 2*3*7. 41 is omitted because 41-1 = 2^3*5.
%e A089189 97 is omitted because 96 = 2^5*3 since higher powers are also tested 
               for
%e A089189 exclusion.
%o A089189 (PARI) powerfreep(n,p) = { c=0; pc=0; forprime(x=2,n, pc++; if(ispowerfree(x-1,
               p), c++; \ print1(x","); ) ); print(); print(c","pc","c/pc+.0) } 
               ispowerfree(m,p1) = { flag=1; y=component(factor(m),2); for(i=1,length(y), 
               if(y[i] >= p1,flag=0;break); ); return(flag) }
%Y A089189 Sequence in context: A109611 A078133 A167773 this_sequence A038612 A012883 
               A002267
%Y A089189 Adjacent sequences: A089186 A089187 A089188 this_sequence A089190 A089191 
               A089192
%K A089189 easy,nonn
%O A089189 1,1
%A A089189 Cino Hilliard (hillcino368(AT)gmail.com), Dec 08 2003