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A239626
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Factored over the Gaussian integers, n has a(n) prime factors counted multiply, including units -1, i, and -i.
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3
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1, 3, 1, 5, 3, 4, 1, 7, 2, 5, 1, 6, 3, 4, 4, 8, 3, 5, 1, 7, 2, 4, 1, 8, 5, 5, 3, 6, 3, 6, 1, 11, 2, 5, 4, 7, 3, 4, 4, 8, 3, 5, 1, 6, 5, 4, 1, 9, 2, 7, 4, 7, 3, 6, 4, 8, 2, 5, 1, 8, 3, 4, 3, 13, 5, 5, 1, 7, 2, 6, 1, 9, 3, 5, 6, 6, 2, 6, 1, 11, 4, 5, 1, 7, 5, 4, 4
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OFFSET
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1,2
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COMMENTS
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Here -1, i, and -i are counted as factors. The factor 1 is counted only in a(1).
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LINKS
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EXAMPLE
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a(2) = 3 because 2 = -i * (1 + i)^2.
a(3) = 1 because 3 is prime over the complex numbers.
a(4) = 5 because 4 = -1 * (1 + i)^4.
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MATHEMATICA
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Table[Total[Transpose[FactorInteger[n, GaussianIntegers -> True]][[2]]], {n, 100}]
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CROSSREFS
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Cf. A239627 (Gaussian factorization including units).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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