A090332 Numbers with no divisors >1 that are prefixes of other divisors in binary representation.
1, 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 33, 35, 37, 41, 43, 47, 49, 53, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 121, 125, 127, 129, 131, 133, 137, 139, 141, 143, 145, 149, 151, 155, 157, 161, 163, 167, 169, 173, 179, 181
Offset: 1
Examples
Divisors >1 of a(188)=637: {7,13,49,91,637}, in binary: {111, 1101, 110001, 1011011, 1001111101}.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
-
Maple
filter:= proc(n) local d, i,j; d:= numtheory:-divisors(n); for i in d do for j from 1 to ilog2(i)-1 do if member(floor(i/2^j), d) then return false fi od od; true end proc: select(filter, [$1..200]); # Robert Israel, Jul 08 2020 -
Mathematica
filterQ[n_] := Catch@Module[{d = Divisors[n], j}, Do[ For[j = 1, j <= Floor@Log[2, i]-1, j++, If[MemberQ[d, Floor[i/2^j]], Throw[False]]], {i, d}]; True]; Select[Range[200], filterQ] (* Jean-François Alcover, Dec 15 2021, after Robert Israel *)
Extensions
Missing term 121 inserted by Robert Israel, Jul 08 2020
Comments