Search: id:A054844
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%I A054844
%S A054844 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,
%T A054844 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,
%U A054844 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
%N A054844 Number of ways to write n as the sum of any number of consecutive integers 
               (including the trivial one-term sum n = n).
%C A054844 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). - Andy Niedermaier (aniedermaier(AT)hmc.edu), 
               Jul 20 2003
%F A054844 Moebius transform is period 2 sequence [2, 0, ...]. - Michael Somos Sep 
               20 2005
%F A054844 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
%e A054844 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.
%o A054844 (PARI) a(n)=2*sumdiv(n,d,d%2)
%Y A054844 A054844(n)=2*A001227(n). Cf. A054843.
%Y A054844 Sequence in context: A082991 A100008 A102763 this_sequence A057936 A033097 
               A036845
%Y A054844 Adjacent sequences: A054841 A054842 A054843 this_sequence A054845 A054846 
               A054847
%K A054844 easy,nonn
%O A054844 1,1
%A A054844 Henry Bottomley (se16(AT)btinternet.com), Apr 13 2000
%E A054844 Corrected and extended by Michael Somos, Apr 26, 2000.

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