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Search: id:A064097
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| A064097 |
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A quasi-logarithm defined inductively by a(1) = 0 and a(p) = 1 + a(p-1) if p is prime and a(n*m) = a(n) + a(m) if m,n > 1. |
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+0
9
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| 0, 1, 2, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 6, 6, 7, 6, 7, 5, 7, 6, 7, 6, 7, 7, 7, 6, 7, 7, 8, 7, 7, 8, 9, 6, 8, 7, 7, 7, 8, 7, 8, 7, 8, 8, 9, 7, 8, 8, 8, 6, 8, 8, 9, 7, 9, 8, 9, 7, 8, 8, 8, 8, 9, 8, 9, 7, 8, 8, 9, 8, 8, 9, 9, 8, 9, 8, 9, 9, 9, 10, 9, 7, 8, 9, 9, 8, 9, 8, 9, 8
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Note that this is the logarithm of a completely multiplicative function. - Michael Somos
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LINKS
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Hugo Pfoertner, Addition chains
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FORMULA
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Conjectures: for n>1, log(n) < a(n) < (5/2)*log(n); lim n ->infinity sum(k=1, n, a(k))/(n*log(n)-n) = C = 1.8(4)... - Benoit Cloitre, Oct 30 2002.
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PROGRAM
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(PARI) oo=200; an=vector(oo); a(n)=an[n]; for(n=2, oo, an[n]=if(isprime(n), 1+a(n-1), sumdiv(n, p, if(isprime(p), a(p)*valuation(n, p))))); for(n=1, 100, print1(a(n)", "))
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CROSSREFS
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Similar to A061373 which uses the same recurrence relation but a(1) = 1.
Cf. A003313, A076142, A076091, A061373, A005245.
For records see A105017.
Adjacent sequences: A064094 A064095 A064096 this_sequence A064098 A064099 A064100
Sequence in context: A003313 A117497 A117498 this_sequence A014701 A056239 A100197
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KEYWORD
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nonn
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AUTHOR
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Thomas Schulze (jazariel(AT)tiscalenet.it), Sep 16 2001
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EXTENSIONS
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More terms from Michael Somos, Sep 25 2001
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