A245788 n times the number of 1's in the binary expansion of n.

0, 1, 2, 6, 4, 10, 12, 21, 8, 18, 20, 33, 24, 39, 42, 60, 16, 34, 36, 57, 40, 63, 66, 92, 48, 75, 78, 108, 84, 116, 120, 155, 32, 66, 68, 105, 72, 111, 114, 156, 80, 123, 126, 172, 132, 180, 184, 235, 96, 147, 150, 204, 156, 212, 216, 275, 168, 228, 232, 295, 240

Offset: 0

Author

Franklin T. Adams-Watters, Aug 01 2014

Keywords

• nonn
• base

Examples

			G.f. = x + 2*x^2 + 6*x^3 + 4*x^4 + 10*x^5 + 12*x6 + 21*x^7 + 8*x^8 + 18*x^9 + ...
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 0..1000
• Project Euler, Problem 759, sequence f(n).

Crossrefs

Cf. A000120 (number of 1's), A057147 (decimal version).

Programs

Maple

a:= n -> n * convert(convert(n,base,2),`+`):
seq(a(n),n=0..100); # Robert Israel, Aug 01 2014

Mathematica

Table[n*DigitCount[n,2,1],{n,0,100}] (* Harvey P. Dale, Dec 16 2014 *)

PARI

sumbit(n) = my(r);while(n>0,r+=n%2;n\=2);r
a(n) = n*sumbit(n)

PARI

{a(n) = if( n<0, 0, n * sumdigits(n, 2))}; /* Michael Somos, Aug 05 2014 */ /* since version 2.6.0 */

Python

[n*bin(n)[2:].count('1') for n in range(1000)] # Chai Wah Wu, Aug 03 2014

Formula

a(2*n) = 2*a(n).

a(2*n+1) = 2*n + 1 + (2+1/n)*a(n). - Robert Israel, Aug 01 2014

G.f.: x * (d/dx) (1/(1 - x))*Sum_{k>=0} x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Mar 27 2018