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A071321
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Alternating sum of all prime factors of n; primes nondecreasing, starting with the least prime factor: A020639(n).
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38
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0, 2, 3, 0, 5, -1, 7, 2, 0, -3, 11, 3, 13, -5, -2, 0, 17, 2, 19, 5, -4, -9, 23, -1, 0, -11, 3, 7, 29, 4, 31, 2, -8, -15, -2, 0, 37, -17, -10, -3, 41, 6, 43, 11, 5, -21, 47, 3, 0, 2, -14, 13, 53, -1, -6, -5, -16, -27, 59, -2, 61, -29, 7, 0, -8
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OFFSET
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1,2
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COMMENTS
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a(n) = 0 iff n square, a(A000290(n)) = 0;
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LINKS
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FORMULA
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EXAMPLE
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72 = 2*2*2*3*3, therefore a(72) = 2 - 2 + 2 - 3 + 3 = 2;
90 = 2*3*3*5, therefore a(90) = 2 - 3 + 3 - 5 = -3.
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MATHEMATICA
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Join[{0}, Table[Total[Times@@@Partition[Riffle[Flatten[Table[#[[1]], {#[[2]]}]&/@ FactorInteger[n]], {1, -1}, {2, -1, 2}], 2]], {n, 2, 100}]] (* Harvey P. Dale, Sep 23 2015 *)
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PROG
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(Haskell)
a071321 1 = 0
a071321 n = sum $ zipWith (*) a033999_list $ a027746_row n
(Python)
from sympy import factorint
fs = factorint(n, multiple=True)
return sum(fs[::2])-sum(fs[1::2]) # Chai Wah Wu, Aug 23 2021
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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