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A079635
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Sum of (2 - p mod 4) for all prime factors p of n (with repetition).
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8
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0, 0, -1, 0, 1, -1, -1, 0, -2, 1, -1, -1, 1, -1, 0, 0, 1, -2, -1, 1, -2, -1, -1, -1, 2, 1, -3, -1, 1, 0, -1, 0, -2, 1, 0, -2, 1, -1, 0, 1, 1, -2, -1, -1, -1, -1, -1, -1, -2, 2, 0, 1, 1, -3, 0, -1, -2, 1, -1, 0, 1, -1, -3, 0, 2, -2, -1, 1, -2, 0, -1, -2, 1, 1, 1, -1, -2, 0, -1, 1, -4, 1, -1, -2, 2, -1, 0, -1, 1
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OFFSET
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1,9
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COMMENTS
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a(n) = {number of primes of the form 4k+1 dividing n} minus {number of primes of the form 4k+3 dividing n}, both counted with multiplicity. - Antti Karttunen, Feb 03 2016, after the formula.
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LINKS
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FORMULA
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Other identities. For all n >= 1:
Totally additive with a(2) = 0, a(p) = 1 if p == 1 (mod 4), and a(p) = -1 if p == 3 (mod 4). - Amiram Eldar, Jun 17 2024
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EXAMPLE
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a(55) = a(5*11) = (2 - 5 mod 4)+(2 - 11 mod 4) = (2-1)+(2-3) = (1)+(-1) = 0.
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MAPLE
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f:= proc(n) local t;
add(t[2]*(2-(t[1] mod 4)), t=ifactors(n)[2])
end proc:
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MATHEMATICA
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f[n_]:=Plus@@((2-Mod[#[[1]], 4])*#[[2]]&/@If[n==1, {}, FactorInteger[n]]); Table[f[n], {n, 100}] (* Ray Chandler, Dec 20 2011 *)
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PROG
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(Haskell)
a079635 1 = 0
a079635 n = sum $ map ((2 - ) . (`mod` 4)) $ a027746_row n
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CROSSREFS
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Cf. A005094 (difference when counting only distinct primes).
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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