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A307908
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a(n) is the least k such that p^k >= n for any prime factor p of n.
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2
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1, 1, 2, 1, 3, 1, 3, 2, 4, 1, 4, 1, 4, 3, 4, 1, 5, 1, 5, 3, 5, 1, 5, 2, 5, 3, 5, 1, 5, 1, 5, 4, 6, 3, 6, 1, 6, 4, 6, 1, 6, 1, 6, 4, 6, 1, 6, 2, 6, 4, 6, 1, 6, 3, 6, 4, 6, 1, 6, 1, 6, 4, 6, 3, 7, 1, 7, 4, 7, 1, 7, 1, 7, 4, 7, 3, 7, 1, 7, 4, 7, 1, 7, 3, 7, 5, 7
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OFFSET
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2,3
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LINKS
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FORMULA
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a(n) = ceiling(log(n)/log(A020639(n))).
a(p^k) = k for any prime number p and any k > 0.
0 <= k*a(n) - a(n^k) < k for any n > 1 and k > 0.
a(n) = 1 iff n is a prime number (A000040).
a(n) = 2 iff n is the square of a prime number (A001248).
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EXAMPLE
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For n = 12:
- the prime factors of 12 are 2 and 3,
- 3^4 > 2^4 >= 12 > 2^3,
- hence a(n) = 4.
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MATHEMATICA
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Array[If[PrimeQ@ #, 1, Ceiling@ Log[FactorInteger[#][[1, 1]], #]] &, 105, 2] (* Michael De Vlieger, May 08 2019 *)
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PROG
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(PARI) a(n) = my (f=factor(n)); logint(n, f[1, 1]) + if (#f~>1, 1, 0)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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