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A143264
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.
3
3, 4, 6, 7, 9, 10, 14, 15, 16, 18, 20, 21, 22, 26, 27, 30, 31, 32, 42, 46, 48, 54, 55, 58, 62, 63, 64, 68, 72, 75, 78, 84, 85, 86, 87, 90, 91, 93, 94, 95, 102, 105, 106, 110, 111, 112, 114, 118, 119, 120, 122, 123, 125, 126, 127, 132, 144, 147, 148, 150, 154, 160, 164
OFFSET
1,1
LINKS
EXAMPLE
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.
MAPLE
filter:= proc(n) local L, t, Lt, m, mt;
L:= convert(n, base, 2);
m:= nops(L);
Lt:= convert(numtheory:-tau(n), base, 2);
mt:= nops(Lt);
andmap(i -> L[i..i+mt-1]<>Lt, [$1..m-mt+1]);
end proc:
select(filter, [$1..1000]); # Robert Israel, Jun 17 2021
MATHEMATICA
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 *)
Select[Range[200], SequenceCount[IntegerDigits[#, 2], IntegerDigits[DivisorSigma[0, #], 2]]==0&] (* Harvey P. Dale, Oct 13 2024 *)
CROSSREFS
Sequence in context: A068675 A190858 A026315 * A126332 A039026 A123540
KEYWORD
base,nonn
AUTHOR
Leroy Quet, Aug 03 2008
EXTENSIONS
Extended by Ray Chandler, Nov 09 2008
STATUS
approved