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%I #8 Oct 28 2013 07:17:23
%S 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,23,25,26,27,28,
%T 29,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,49,50,51,52,53,54,
%U 55,57,58,59,61,62,63,64,65,66,67,68,69,70,71,73,74,75,76,77,78
%N Numbers n which have a prime divisor p such that 1 is the only positive integer which divides n/p^m and is congruent to 1 modulo p, where p^(m+1) does not divide n.
%C The solvability of a group whose order is a(n) can be reduced to the solvability of smaller group using the Sylow theorems, provided the order is not a prime.
%C 80 is not a member of this sequence, but is a member of A168186. - Franklin T. Adams-Watters, Jan 26 2010
%H Charles R Greathouse IV, <a href="/A160453/b160453.txt">Table of n, a(n) for n = 1..10000</a>
%o (PARI) is(n)=if(n<12,return(n>0));my(f=factor(n)); for(i=1,#f~, fordiv(n/f[i,1]^f[i,2],d, if(d>1&&d%f[i,1]==1,next(2))); return(1)); 0 \\ _Charles R Greathouse IV_, Oct 27 2013
%Y All three of A023805, A160453, A168186 are different.
%K nonn
%O 1,2
%A _Masahiko Shin_, May 14 2009
%E Corrected by _Charles R Greathouse IV_, Oct 27 2013
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