%I
%S 2,3,4,7,15,23,39,63,75,87,111,135,147,159,195,219,231,255,267,315,
%T 387,399,411,423,435,447,459,495,519,567,615,663,675,699,711,735,747,
%U 759,771,819,867,915,999,1011,1023,1035,1047,1071,1095,1119,1155,1167,1263
%N Numbers n such that n  2^k is squarefree for all 1 <= 2^k < n.
%C Erdos conjectures that this sequence is infinite. It appears that n = 3 (mod 12) except for n = 2, 4, 7 and 23.
%D R. K. Guy, Unsolved Problems in Number Theory, A19.
%H T. D. Noe, <a href="/A091155/b091155.txt">Table of n, a(n) for n = 1..10000</a>
%H P. Erdõs, <a href="http://www.renyi.hu/~p_erdos/195007.pdf">On integers of the form 2^k + p and some related problems</a>, Summa Brasil. Math. 2 (1950), pp. 113123.
%e 39 is on the list because 38, 37, 35, 31, 23 and 7 are all squarefree.
%t a={}; Do[k=1; While[sf=SquareFreeQ[nk]; sf&&2k<n, k=2k]; If[sf, AppendTo[a, n]], {n, 2000}]; a
%o (PARI) is(n)=for(k=1,log(n+.5)\log(2),if(!issquarefree(n2^k),return(0))); 1 \\ _Charles R Greathouse IV_, Apr 13 2014
%Y Cf. A039669 (n such that n2^k are all primes).
%K nonn
%O 1,1
%A _T. D. Noe_, Dec 23 2003
