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A071188
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Largest prime factor of number of divisors of n; a(1)=1.
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5
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1, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 5, 2, 3, 2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 5, 3, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 7, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 3, 2, 2, 2, 5, 5, 2, 2, 3, 2, 2, 2, 2, 2, 3
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OFFSET
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1,2
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COMMENTS
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a(n)=2 if and only if every member of the prime signature of n is of the form 2^k-1.
a(m*k) = max(a(m),a(k)) if m and k are coprime. (End)
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LINKS
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FORMULA
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Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*d(1) + Sum_{k>=2} prime(k)*(d(k) - d(k-1)) = 2.4365518864..., where d(1) = A327839, and for k >= 2, d(k) is the asymptotic density of numbers whose number of divisors is a prime(k)-smooth number, i.e., d(k) = Product_{p prime} ((1 - 1/p) * Sum_{i, A006530(i) <= prime(k)} 1/p^(i-1)) (see A354181 for an example). - Amiram Eldar, Jan 15 2024
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MAPLE
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f:= n -> max(1, numtheory:-factorset(numtheory:-tau(n))):
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MATHEMATICA
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Max[Transpose[FactorInteger[#]][[1]]]&/@DivisorSigma[0, Range[100]] (* Harvey P. Dale, Aug 28 2013 *)
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PROG
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(Haskell)
(PARI) a(n) = if(n == 1, 1, vecmax(factor(numdiv(n))[, 1])); \\ Michel Marcus, Dec 05 2016
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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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