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A363619
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Weighted alternating sum of the multiset of prime indices of n.
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8
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0, 1, 2, -1, 3, -3, 4, 2, -2, -5, 5, 5, 6, -7, -4, -2, 7, 3, 8, 8, -6, -9, 9, -6, -3, -11, 4, 11, 10, 6, 11, 3, -8, -13, -5, -3, 12, -15, -10, -10, 13, 9, 14, 14, 7, -17, 15, 8, -4, 4, -12, 17, 16, -5, -7, -14, -14, -19, 17, -7, 18, -21, 10, -3, -9, 12, 19, 20
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OFFSET
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1,3
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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.
We define the weighted alternating sum of a sequence (y_1,...,y_k) to be Sum_{i=1..k} (-1)^(i-1) i * y_i.
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LINKS
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EXAMPLE
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The prime indices of 300 are {1,1,2,3,3}, with weighted alternating sum 1*1 - 2*1 + 3*2 - 4*3 + 5*3 = 8, so a(300) = 8.
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MATHEMATICA
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prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
altwtsum[y_]:=Sum[(-1)^(k-1)*k*y[[k]], {k, 1, Length[y]}];
Table[altwtsum[prix[n]], {n, 100}]
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CROSSREFS
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A359677 gives zero-based weighted sum of prime indices, reverse A359674.
Cf. A000009, A000720, A001221, A046660, A053632, A106529, A124010, A181819, A261079, A363532, A363621, A363626.
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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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