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

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, 49, 56, 60, 62, 63, 64, 66, 70, 72, 75, 84, 90, 93, 96, 98, 105, 112, 120, 124, 126, 127, 128, 129, 132, 133, 135, 140, 144, 150, 155, 161, 165, 168, 180, 186, 189, 192, 195, 196

Offset

1,2

Comments

Contains m*(2^k-1) for 1 <= m <= 2^k + 2 and any k >= 1. - Robert Israel, Aug 04 2016

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Scatterplot of the first 10000 terms of the first difference of A100290 (cf. A292777)

Example

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

Maple

filter:= n -> evalb(n mod (2^numboccur(1, convert(n, base, 2))-1) = 0):
select(filter, [$1..1000]); # Robert Israel, Aug 04 2016

Mathematica

Select[Range[200], Divisible[#, 2^DigitCount[#, 2, 1] - 1] &] (* Ivan Neretin, Aug 03 2016 *)

Prog

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

Crossrefs

Cf. A038573, A292777.

Sequence in context: A004742 A277817 A336231 * A344341 A140181 A038032

Adjacent sequences: A100287 A100288 A100289 * A100291 A100292 A100293

Keyword

base,easy,nonn

Author

Marc LeBrun, Nov 11 2004

Status

approved