cp's OEIS Frontend

A100290 Numbers divisible by smallest number with same number of 1's in its binary expansion. That is, A038573(a(n)) divides a(n).

%I A100290 #16 Oct 08 2017 12:58:19
%S A100290 1,2,3,4,6,7,8,9,12,14,15,16,18,21,24,28,30,31,32,33,35,36,42,45,48,
%T A100290 49,56,60,62,63,64,66,70,72,75,84,90,93,96,98,105,112,120,124,126,127,
%U A100290 128,129,132,133,135,140,144,150,155,161,165,168,180,186,189,192,195,196
%N A100290 Numbers divisible by smallest number with same number of 1's in its binary expansion. That is, A038573(a(n)) divides a(n).
%C A100290 Contains m*(2^k-1) for 1 <= m <= 2^k + 2 and any k >= 1. - _Robert Israel_, Aug 04 2016
%H A100290 Ivan Neretin, <a href="/A100290/b100290.txt">Table of n, a(n) for n = 1..10000</a>
%H A100290 Rémy Sigrist, <a href="/A100290/a100290.png">Scatterplot of the first 10000 terms of the first difference of A100290</a> (cf. A292777)
%e A100290 21 is a member since 21 = 10101 base 2, which is divisible by 7 = 111 base 2.
%p A100290 filter:= n -> evalb(n mod (2^numboccur(1,convert(n,base,2))-1) = 0):
%p A100290 select(filter, [$1..1000]); # _Robert Israel_, Aug 04 2016
%t A100290 Select[Range[200], Divisible[#, 2^DigitCount[#, 2, 1] - 1] &] (* _Ivan Neretin_, Aug 03 2016 *)
%o A100290 (PARI) is(n)=n%(2^hammingweight(n)-1)==0 \\ _Charles R Greathouse IV_, Aug 04 2016
%Y A100290 Cf. A038573, A292777.
%K A100290 base,easy,nonn
%O A100290 1,2
%A A100290 _Marc LeBrun_, Nov 11 2004