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A343938
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Twice the number of prime factors of n minus the sum of prime indices of n, both counted with multiplicity.
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4
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0, 1, 0, 2, -1, 1, -2, 3, 0, 0, -3, 2, -4, -1, -1, 4, -5, 1, -6, 1, -2, -2, -7, 3, -2, -3, 0, 0, -8, 0, -9, 5, -3, -4, -3, 2, -10, -5, -4, 2, -11, -1, -12, -1, -1, -6, -13, 4, -4, -1, -5, -2, -14, 1, -4, 1, -6, -7, -15, 1, -16, -8, -2, 6, -5, -2, -17, -3, -7
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OFFSET
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1,4
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
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LINKS
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FORMULA
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Totally additive with a(prime(k)) = 2 - k.
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EXAMPLE
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For n = 1050 we have 5 prime indices {1,2,3,3,4}, so a(1050) = 10 - 13 = -3.
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MATHEMATICA
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Table[2*PrimeOmega[n]-Total[Cases[FactorInteger[n], {p_, k_}:>k*PrimePi[p]]], {n, 100}]
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CROSSREFS
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First appearances are the elements of A174090 except for 3.
Positions of nonpositive terms are A344291.
Positions of nonnegative terms are A344296.
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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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