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A071825
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(Number of x with largest prime factor of the form 4k+3 less than or equal to n) minus (Number of x with largest prime factor of the form 4k+1 less than or equal to n).
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0
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0, 1, 1, 0, 1, 2, 2, 3, 2, 3, 4, 3, 4, 3, 3, 2, 3, 4, 3, 4, 5, 6, 7, 6, 5, 6, 7, 6, 5, 6, 6, 7, 6, 7, 8, 7, 8, 7, 6, 5, 6, 7, 8, 7, 8, 9, 10, 11, 10, 9, 8, 7, 8, 9, 10, 11, 10, 11, 10, 9, 10, 11, 11, 10, 11, 12, 11, 12, 13, 14, 15, 14, 13, 12, 13, 14, 13, 14, 13, 14, 13, 14, 15, 14, 15, 14, 15
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OFFSET
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1,6
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COMMENTS
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Weak conjecture: sequence gives positive values only; strong conjecture: for n large enough a(n) > 2*sqrt(n).
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LINKS
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FORMULA
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a(n) = Card( x<=n : A006530(x) == 3 mod 4) - Card( x<=n : A006530(x) == 1 mod 4)
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PROG
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(PARI) for(n=2, 200, print1(sum(i=2, n, if((component(component(factor(i), 1), omega(i))-3)%4, 0, 1))-sum(i=2, n, if((component(component(factor(i), 1), omega(i))-1)%4, 0, 1)), ", "))
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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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STATUS
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approved
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