The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A089042 Composite numbers such that all divisors >1 have the same number of 1's in binary representation. 2
 4, 8, 9, 16, 32, 49, 64, 128, 133, 256, 259, 512, 961, 1024, 2048, 2059, 2449, 3713, 4096, 4681, 4867, 6169, 6241, 8192, 8401, 8773, 9353, 10261, 10561, 12307, 12449, 16129, 16384, 16459, 16531, 16771, 18467, 20491, 24649, 24721, 24961, 25217 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A000120(d)=constant for all d with 12 up to 10000000. - Michel Marcus, Jun 05 2013 From Robert Israel, Dec 01 2015: (Start) The only term divisible by 3 is 9. The terms divisible by 2 are 2^k for k > 1. There are no terms divisible by 5. (End) LINKS Harvey P. Dale and Robert Israel, Table of n, a(n) for n = 1..1000 (a(1) to a(100) from Harvey P. Dale) EXAMPLE Divisors >1 of 259: 7, 37 and 259, which have all three 1's in binary: 7->'111', 37->'100101' and 259->'100000011', therefore 259 is a term. MAPLE A000120:= proc(n) convert(convert(n, base, 2), `+`) end proc: filter:= proc(n) local t, f; if isprime(n) then return false fi; if n::even then return evalb(n = 2^ilog2(n)) fi; if n mod 3 = 0 then return evalb(n = 9) fi; t:= A000120(n); for f in numtheory:-divisors(n) minus {1, n} do   if A000120(f) <> t then return false fi; od; true end proc: select(filter, [\$4..10^5]); # Robert Israel, Dec 01 2015 MATHEMATICA dn1Q[n_]:=!PrimeQ[n]&&Length[Union[(DigitCount[#, 2, 1]&/@Rest[Divisors[ n]])]] == 1; Select[Range[26000], dn1Q] (* Harvey P. Dale, Oct 03 2013 *) PROG isok(n) = {if (isprime(n), return (0), nb = norml2(binary(n)); fordiv(n, d, if (d!=1 && norml2(binary(d)) != nb, return (0))); return (1); ); }  \\ Michel Marcus, Jun 05 2013 CROSSREFS Cf. A007088, A002808. Sequence in context: A272758 A227645 A285438 * A340093 A227243 A272575 Adjacent sequences:  A089039 A089040 A089041 * A089043 A089044 A089045 KEYWORD nonn,base AUTHOR Reinhard Zumkeller, Dec 02 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 18 03:03 EDT 2021. Contains 343994 sequences. (Running on oeis4.)