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%I #10 Jun 18 2021 01:14:17
%S 3,4,6,7,9,10,14,15,16,18,20,21,22,26,27,30,31,32,42,46,48,54,55,58,
%T 62,63,64,68,72,75,78,84,85,86,87,90,91,93,94,95,102,105,106,110,111,
%U 112,114,118,119,120,122,123,125,126,127,132,144,147,148,150,154,160,164
%N A positive integer n is included if the binary representation of the number of divisors of n does not occur anywhere in the binary representation of n.
%H Robert Israel, <a href="/A143264/b143264.txt">Table of n, a(n) for n = 1..10000</a>
%e 30 has 8 divisors. 30 in binary is 11110. 8 in binary is 1000. The string 1000 does not occur anywhere in the string 11110. So 30 occurs in this sequence.
%p filter:= proc(n) local L,t,Lt,m, mt;
%p L:= convert(n,base,2);
%p m:= nops(L);
%p Lt:= convert(numtheory:-tau(n),base,2);
%p mt:= nops(Lt);
%p andmap(i -> L[i..i+mt-1]<>Lt, [$1..m-mt+1]);
%p end proc:
%p select(filter, [$1..1000]); # _Robert Israel_, Jun 17 2021
%t bndQ[n_]:=Module[{bn=IntegerDigits[n,2],dn=IntegerDigits[ DivisorSigma[ 0,n],2]}, !MemberQ[ Partition[ bn,Length[dn],1],dn]]; Select[Range[ 200],bndQ] (* _Harvey P. Dale_, Nov 01 2013 *)
%Y Cf. A143262, A143263.
%K base,nonn
%O 1,1
%A _Leroy Quet_, Aug 03 2008
%E Extended by _Ray Chandler_, Nov 09 2008
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