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A061373
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"Natural" logarithm, defined inductively by a(1)=1, a(p) = 1 + a(p-1) if p is prime and a(n*m) = a(n) + a(m) if n, m>1.
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9
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1, 2, 3, 4, 5, 5, 6, 6, 6, 7, 8, 7, 8, 8, 8, 8, 9, 8, 9, 9, 9, 10, 11, 9, 10, 10, 9, 10, 11, 10, 11, 10, 11, 11, 11, 10, 11, 11, 11, 11, 12, 11, 12, 12, 11, 13, 14, 11, 12, 12, 12, 12, 13, 11, 13, 12, 12, 13, 14, 12, 13, 13, 12, 12, 13, 13, 14, 13, 14, 13, 14, 12, 13, 13, 13, 13, 14
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OFFSET
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1,2
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COMMENTS
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Related to A005245, the complexity of n, which is <= this sequence. They are equal up to term a(46) and for 771 values out of the first 1000 terms. A061373 is easier to compute.
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LINKS
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MATHEMATICA
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a[1]=1; a[p_?PrimeQ] := 1+a[p-1]; a[n_] := a[n] = With[{d=Divisors[n][[2]] }, a[d] + a[n/d]]; Array[a, 100] (* Jean-François Alcover, Feb 26 2016 *)
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PROG
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(Haskell)
import Data.List (genericIndex)
a061373 1 = 1
a061373 n = genericIndex a061373_list (n-1)
a061373_list = 1 : f 2 where
f x | x == spf = 1 + a061373 (spf - 1) : f (x + 1)
| otherwise = a061373 spf + a061373 (x `div` spf) : f (x + 1)
where spf = a020639 x
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CROSSREFS
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KEYWORD
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easy,nice,nonn
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AUTHOR
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STATUS
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approved
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