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A058060
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Number of distinct prime factors of d(n), the number of divisors of n.
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6
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0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1
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OFFSET
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1,12
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COMMENTS
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The sums of the first 10^k terms, for k = 1, 2, ..., are 9, 122, 1285, 13096, 131729, 1319621, 13203252, 132055132, 1320621032, 13206429426, 132064984784, ... . From these values the asymptotic mean of this sequence, whose existence was proven by Rieger (1972) and Heppner (1974) (see the Formula section), can be empirically evaluated by 1.3206... . - Amiram Eldar, Jan 15 2024
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REFERENCES
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József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter V, page 164.
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) = c * n + O(sqrt(n) * log(n)^5), where c is a constant (Rieger, 1972; Heppner, 1974). - Amiram Eldar, Jan 15 2024
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EXAMPLE
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n = 120 = 8*3*5, d(n) = 16 = 2^4, so a(120)=1.
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MATHEMATICA
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Table[PrimeNu[DivisorSigma[0, n]], {n, 1, 100}] (* G. C. Greubel, May 05 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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EXTENSIONS
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STATUS
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approved
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