Search: id:A064097
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%I A064097
%S A064097 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,
%T A064097 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,
%U A064097 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
%N A064097 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.
%C A064097 Note that this is the logarithm of a completely multiplicative function. 
               - Michael Somos
%H A064097 Hugo Pfoertner, <a href="a003313.txt">Addition chains</a>
%F A064097 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.
%o A064097 (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)","))
%Y A064097 Similar to A061373 which uses the same recurrence relation but a(1) = 
               1.
%Y A064097 Cf. A003313, A076142, A076091, A061373, A005245.
%Y A064097 For records see A105017.
%Y A064097 Sequence in context: A003313 A117497 A117498 this_sequence A014701 A056239 
               A161511
%Y A064097 Adjacent sequences: A064094 A064095 A064096 this_sequence A064098 A064099 
               A064100
%K A064097 nonn
%O A064097 1,3
%A A064097 Thomas Schulze (jazariel(AT)tiscalenet.it), Sep 16 2001
%E A064097 More terms from Michael Somos, Sep 25 2001

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