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A273711
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The Hadamard product of omega(n) and A007875(n).
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1
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0, 1, 1, 1, 1, 4, 1, 1, 1, 4, 1, 4, 1, 4, 4, 1, 1, 4, 1, 4, 4, 4, 1, 4, 1, 4, 1, 4, 1, 12, 1, 1, 4, 4, 4, 4, 1, 4, 4, 4, 1, 12, 1, 4, 4, 4, 1, 4, 1, 4, 4, 4, 1, 4, 4, 4, 4, 4, 1, 12, 1, 4, 4, 1, 4, 12, 1, 4, 4, 12, 1, 4, 1, 4, 4, 4, 4, 12, 1, 4, 1, 4, 1, 12, 4
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OFFSET
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1,6
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COMMENTS
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Total number of distinct prime factors of the squarefree divisors of n. Inverse Möbius transform of omega(n)*mu(n)^2. - Wesley Ivan Hurt, Jun 17 2023
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LINKS
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FORMULA
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a(n) = omega(n)*2^(omega(n)-1).
a(n) = Sum_{d|n} omega(d)*mu(d)^2. (End)
Dirichlet g.f.: (zeta(s)^2/zeta(2*s)) * P(s, 1), where P(s, c) = Sum_{p prime} 1/(p^s + c) is the shifted prime zeta function (Wakhare, 2016). - Amiram Eldar, Nov 03 2023
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MAPLE
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end proc:
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MATHEMATICA
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Table[EulerPhi[2^PrimeNu[n]]*PrimeNu[n], {n, 1, 50}] (* G. C. Greubel, May 19 2017 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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