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Search: id:A054844
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| A054844 |
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Number of ways to write n as the sum of any number of consecutive integers (including the trivial one-term sum n = n). |
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+0
3
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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
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FORMULA
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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
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EXAMPLE
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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.
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PROGRAM
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(PARI) a(n)=2*sumdiv(n, d, d%2)
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CROSSREFS
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A054844(n)=2*A001227(n). Cf. A054843.
Sequence in context: A082991 A100008 A102763 this_sequence A057936 A033097 A036845
Adjacent sequences: A054841 A054842 A054843 this_sequence A054845 A054846 A054847
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Apr 13 2000
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EXTENSIONS
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Corrected and extended by Michael Somos, Apr 26, 2000.
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