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

Author

Marc LeBrun, Nov 11 2004

Keywords

• base
• easy
• nonn

Comments

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

Examples

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

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)

Crossrefs

Cf. A038573, A292777.

Programs

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 *)

PARI

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