A161765 a(n) is the smallest multiple of {the number of 1's in the binary representation of n} that is >= n.

1, 2, 4, 4, 6, 6, 9, 8, 10, 10, 12, 12, 15, 15, 16, 16, 18, 18, 21, 20, 21, 24, 24, 24, 27, 27, 28, 30, 32, 32, 35, 32, 34, 34, 36, 36, 39, 39, 40, 40, 42, 42, 44, 45, 48, 48, 50, 48, 51, 51, 52, 54, 56, 56, 55, 57, 60, 60, 60, 60, 65, 65, 66, 64, 66, 66, 69, 68, 69, 72, 72, 72

Offset: 1

Author

Leroy Quet, Jun 18 2009

Keywords

• base
• nonn

Examples

			11 (decimal) in binary is 1011. There are three 1's. Because 12 is the smallest multiple of 3 that is >= 11, then a(11) = 12.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A161764, A000120.

Programs

Maple

a := proc (n) local n2, s, j: n2 := convert(n, base, 2): s := add(n2[i], i = 1 .. nops(n2)): for j while j*s < n do end do: j*s end proc: seq(a(n), n = 1 .. 80); # Emeric Deutsch, Jun 24 2009

Mathematica

Table[d=DigitCount[n,2,1];d*Ceiling[n/d],{n,80}] (* Harvey P. Dale, Aug 23 2013 *)

PARI

a(n) = my(nb = hammingweight(n)); nb*ceil(n/nb); \\ Michel Marcus, Nov 11 2018

Formula

a(n) = A000120(n)*ceiling(n/A000120(n)). - Michel Marcus, Nov 11 2018

Extensions

Extended by Emeric Deutsch, Jun 24 2009