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Search: id:A024919
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| A024919 |
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Sum(k=1..n,(-1)^k*k*floor(n/k)). |
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3
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| -1, 0, -4, 1, -5, -1, -9, 4, -9, -3, -15, 5, -9, -1, -25, 4, -14, -1, -21, 9, -23, -11, -35, 17, -14, 0, -40, 0, -30, -6, -38, 23, -25, -7, -55, 10, -28, -8, -64, 14, -28, 4, -40, 20, -58, -34, -82, 34, -23, 8, -64, 6, -48, -8, -80, 24, -56, -26, -86, 34, -28, 4, -100, 25, -59
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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n - 2*[ n/2 ] + 3*[ n/3 ] - ... + m*n*[ n/n ], where m = (-1)^(n+1).
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FORMULA
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a(n) = 4*A024916(floor(n/2))-A024916(n). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Oct 15 2002
G.f.: 1/(1-x)*Sum_{n>=1} n*x^n*(3*x^n-1)/(1-x^(2*n)). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Oct 15 2002
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MATHEMATICA
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f[n_] := Sum[(-1)^i*i*Floor[n/i], {i, 1, n}]; Table[ f[n], {n, 1, 85}]
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CROSSREFS
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The zeros are A072663.
Partial sums of A002129.
Sequence in context: A107463 A101322 A029644 this_sequence A003415 A086300 A028271
Adjacent sequences: A024916 A024917 A024918 this_sequence A024920 A024921 A024922
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KEYWORD
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sign
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 17 2002
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