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A071860
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Number of k 1<=k<=n such that sigma(k) is odd.
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2
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1, 2, 2, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15
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OFFSET
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1,2
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COMMENTS
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a(n) = number of points in [0, n*Pi/2] where cos(x) cos(x/2) ... cos(x/n) changes sign. - Robert Israel, Apr 29 2011
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REFERENCES
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Richard Crandall and Carl Pomerance, Prime numbers: a computational perspective. Springer-Verlag, New York, 2001, p. 52.
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LINKS
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FORMULA
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a(n) = floor( C * sqrt(n) ) +- 1, 0 with C = 1+1/sqrt(2) = 1.707...
a(n) = floor(sqrt(n)) + floor(sqrt(n/2)). (Crandall and Pomerance). - Franz Vrabec, Jun 24 2006
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MATHEMATICA
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Accumulate[If[OddQ[DivisorSigma[1, #]], 1, 0]&/@Range[90]] (* Harvey P. Dale, Jul 15 2012 *)
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PROG
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(PARI) for(n=1, 100, print1(sum(i=1, n, if(sigma(i)%2, 1, 0)), ", "))
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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