login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A054844 Number of ways to write n as the sum of any number of consecutive integers (including the trivial one-term sum n = n). 9
2, 2, 4, 2, 4, 4, 4, 2, 6, 4, 4, 4, 4, 4, 8, 2, 4, 6, 4, 4, 8, 4, 4, 4, 6, 4, 8, 4, 4, 8, 4, 2, 8, 4, 8, 6, 4, 4, 8, 4, 4, 8, 4, 4, 12, 4, 4, 4, 6, 6, 8, 4, 4, 8, 8, 4, 8, 4, 4, 8, 4, 4, 12, 2, 8, 8, 4, 4, 8, 8, 4, 6, 4, 4, 12, 4, 8, 8, 4, 4, 10, 4, 4, 8, 8, 4, 8, 4, 4, 12, 8, 4, 8, 4, 8, 4, 4, 6, 12, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) = twice the number of odd divisors of n. That is, if d is the divisor function and q is the exponent of the largest power of 2 dividing n, then the a(n) equals 2*d(n)/(q+1). - Andrew Niedermaier, Jul 20 2003

LINKS

Table of n, a(n) for n=1..100.

FORMULA

a(n) = 2*A001227(n). - Andrew Niedermaier, Jul 20 2003

Moebius transform is period 2 sequence [2, 0, ...]. - Michael Somos, Sep 20 2005

G.f.: Sum_{k>0} 2x^k/(1-x^(2k)) = Sum_{k>0} 2x^(2k-1)/(1-x^(2k-1)). - Michael Somos, Sep 20 2005

EXAMPLE

a(3)=4 because 3 = (-2)+(-1)+0+1+2+3 or 0+1+2 or 1+2 or 3; a(13)=4 because 13 = (-12)+...+13 or (-5)+...+7 or 6+7 or 13.

PROG

(PARI) a(n)=2*sumdiv(n, d, d%2)

CROSSREFS

Cf. A054843.

Sequence in context: A214212 A100008 A102763 * A057936 A033097 A036845

Adjacent sequences:  A054841 A054842 A054843 * A054845 A054846 A054847

KEYWORD

easy,nonn

AUTHOR

Henry Bottomley, Apr 13 2000

EXTENSIONS

Corrected and extended by Michael Somos, Apr 26 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 19 02:06 EST 2018. Contains 299330 sequences. (Running on oeis4.)