%I #17 Feb 04 2022 09:39:48

%S 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,

%T 50,52,56,63,64,127,128,129,130,132,135,136,139,141,142,144,147,149,

%U 150,153,154,156,160,163,165,166,169,170,172,177,178,180,184,192,195,197

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

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

%C A000079 and A000225 (> 0) are subsequences.

%H Ivan Neretin, <a href="/A096199/b096199.txt">Table of n, a(n) for n = 1..10674 (all terms up to 2^16)</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

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

%p q:= n-> (l-> irem(nops(l), add(i, i=l))=0)(Bits[Split](n)):

%p select(q, [$1..200])[]; # _Alois P. Heinz_, Feb 04 2022

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

%o (Perl)

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

%Y Cf. A007088, A049445.

%K nonn,base

%O 1,2

%A _Reinhard Zumkeller_, Jul 26 2004