Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Mar 16 2024 05:22:22
%S 1,2,5,7,13,14,17,22,23,26,41,43,53,67,70,71,77,79,122,130,131,133,
%T 134,149,151,157,158,161,202,203,205,206,211,214,215,229,230,233,238,
%U 239,241,365,367,373,374,377,391,394,395,401,403,445,446,449,454,455,457
%N Squarefree numbers that are zeroless in base 3 (A032924).
%C The relative asymptotic density of this sequence within the zeroless numbers in base 3 is 27/(4*Pi^2) = 1/A214549 = 0.683917... (Banks and Shparlinski, 2004).
%H Amiram Eldar, <a href="/A371239/b371239.txt">Table of n, a(n) for n = 1..10000</a>
%H William D. Banks and Igor E. Shparlinski, <a href="http://dx.doi.org/10.4064/aa112-4-1">Arithmetic properties of numbers with restricted digits</a>, Acta Arithmetica, Vol. 112, No. 4 (2004), pp. 313-332; <a href="https://eudml.org/doc/278042">alternative link</a>.
%t Select[Range[500], !MemberQ[IntegerDigits[#, 3], 0] && SquareFreeQ[#] &]
%o (PARI) is(n) = vecmin(digits(n, 3)) > 0 && issquarefree(n);
%Y Intersection of A005117 and A032924.
%Y Cf. A214549, A371240, A371241.
%K nonn,base,easy
%O 1,2
%A _Amiram Eldar_, Mar 16 2024