A096199 Numbers such that in binary representation the length is a multiple of the number of ones.

1, 2, 3, 4, 7, 8, 9, 10, 12, 15, 16, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 44, 48, 49, 50, 52, 56, 63, 64, 127, 128, 129, 130, 132, 135, 136, 139, 141, 142, 144, 147, 149, 150, 153, 154, 156, 160, 163, 165, 166, 169, 170, 172, 177, 178, 180, 184, 192, 195, 197

Offset: 1

Author

Reinhard Zumkeller, Jul 26 2004

Keywords

• nonn
• base

Comments

A070939(a(n)) mod A000120(a(n)) = 0;

A000079 and A000225 (> 0) are subsequences.

Examples

			400 -> '110010000' with 3 binary ones and length = 9 = 3*3, therefore 400 is a term.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10674 (all terms up to 2^16)
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A007088, A049445.

Programs

Maple

q:= n-> (l-> irem(nops(l), add(i, i=l))=0)(Bits[Split](n)):
select(q, [$1..200])[];  # Alois P. Heinz, Feb 04 2022

Mathematica

lmnQ[n_]:=Module[{idn2=IntegerDigits[n,2]},Divisible[Length[idn2],Count[ idn2,1]]]; Select[Range[200],lmnQ] (* Harvey P. Dale, Jul 27 2019 *)

Perl

$cnt=1;foreach $n(1..100_000){$_=sprintf ("%b",$n); print $cnt++," $n\n" unless (length)%s/1//g;}