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 A100290 Numbers divisible by smallest number with same number of 1's in its binary expansion. That is, A038573(a(n)) divides a(n). 3

%I

%S 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 49,56,60,62,63,64,66,70,72,75,84,90,93,96,98,105,112,120,124,126,127,

%U 128,129,132,133,135,140,144,150,155,161,165,168,180,186,189,192,195,196

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

%C Contains m*(2^k-1) for 1 <= m <= 2^k + 2 and any k >= 1. - _Robert Israel_, Aug 04 2016

%H Ivan Neretin, <a href="/A100290/b100290.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A100290/a100290.png">Scatterplot of the first 10000 terms of the first difference of A100290</a> (cf. A292777)

%e 21 is a member since 21 = 10101 base 2, which is divisible by 7 = 111 base 2.

%p filter:= n -> evalb(n mod (2^numboccur(1,convert(n,base,2))-1) = 0):

%p select(filter, [\$1..1000]); # _Robert Israel_, Aug 04 2016

%t Select[Range[200], Divisible[#, 2^DigitCount[#, 2, 1] - 1] &] (* _Ivan Neretin_, Aug 03 2016 *)

%o (PARI) is(n)=n%(2^hammingweight(n)-1)==0 \\ _Charles R Greathouse IV_, Aug 04 2016

%Y Cf. A038573, A292777.

%K base,easy,nonn

%O 1,2

%A _Marc LeBrun_, Nov 11 2004

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Last modified June 5 16:19 EDT 2020. Contains 334852 sequences. (Running on oeis4.)