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A369180
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Alternating sum of the k-adic valuations (ruler functions) of n.
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2
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0, 1, -1, 3, -1, 1, -1, 5, -3, 1, -1, 4, -1, 1, -3, 8, -1, 0, -1, 4, -3, 1, -1, 7, -3, 1, -5, 4, -1, 1, -1, 10, -3, 1, -3, 5, -1, 1, -3, 7, -1, 1, -1, 4, -6, 1, -1, 11, -3, 0, -3, 4, -1, -1, -3, 7, -3, 1, -1, 6, -1, 1, -6, 14, -3, 1, -1, 4, -3, 1, -1, 9, -1, 1, -6, 4, -3, 1
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n) = Sum_{k=2..n} (-1)^k * valuation(n,k).
G.f.: Sum_{k>=2, j>=1} (-1)^k x^(k^j)/(1-x^(k^j)).
Asymptotic mean: lim_{m->oo} (1/m) * Sum_{n=1..m} a(n) = log(2).
Dirichlet g.f.: zeta(s) * Sum_{k>=1} (1 - eta(ks)).
Sum_{n>=1} a(n)/n^2 = Pi^2/24.
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MAPLE
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a:= n-> add((-1)^i*padic[ordp](n, i), i=2..n):
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MATHEMATICA
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z = 70; Sum[(-1)^k IntegerExponent[Range[z], k], {k, 2, z}]
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PROG
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(PARI) a(n) = sum(k=2, n, (-1)^k * valuation(n, k)); \\ Michel Marcus, Jan 18 2024
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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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