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A005094
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Number of distinct primes of the form 4k+1 dividing n minus number of distinct primes of the form 4k+3 dividing n.
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9
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0, 0, -1, 0, 1, -1, -1, 0, -1, 1, -1, -1, 1, -1, 0, 0, 1, -1, -1, 1, -2, -1, -1, -1, 1, 1, -1, -1, 1, 0, -1, 0, -2, 1, 0, -1, 1, -1, 0, 1, 1, -2, -1, -1, 0, -1, -1, -1, -1, 1, 0, 1, 1, -1, 0, -1, -2, 1, -1, 0, 1, -1, -2, 0, 2, -2, -1, 1, -2, 0, -1, -1, 1, 1, 0, -1, -2, 0, -1, 1, -1
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OFFSET
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1,21
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LINKS
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FORMULA
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Additive with a(p^e) = 0 if p = 2, 1 if p == 1 (mod 4), -1 if p == 3 (mod 4).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = -A086239 = -0.334981... . - Amiram Eldar, Jan 02 2024
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MATHEMATICA
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Join[{0}, Table[Total[Which[Mod[#, 4]==1, 1, Mod[#, 4]==3, -1, True, 0]&/@ FactorInteger[ n][[All, 1]]], {n, 2, 100}]] (* Harvey P. Dale, Sep 03 2022 *)
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PROG
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(Haskell)
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CROSSREFS
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Cf. A079635 (difference when counted with multiplicity).
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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