Search: id:A102048
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%I A102048
%S A102048 1,1,1,2,1,2,1,5,3,2,1,5,1,2,3,12,1,7,1,4,3,2,1,10,5,2,11,4,1,7,1,27,3,
%T A102048 2,5,16,1,2,3,9,1,6,1,4,10,2,1,22,7,11,3,4,1,24,5,9,3,2,1,14,1,2,10,58,
%U A102048 5,6,1,4,3,11,1,33,1,2,17,4,7,6,1,19,37,2,1,13,5,2,3,8,1,21,7,4,3,2,5
%N A102048 Exponent of A046021(n) (least inverse of Kempner-Smarandache function 
               A002034) when written as a power of A006530(n) (largest prime dividing 
               n), with a(1) = 1.
%C A102048 a(n) = log(A046021(n))/log(A006530(n)) for n>1.
%D A102048 R. L. Graham, D. E. Knuth and O. Patashnik, Factorial Factors, Section 
               4.4 in Concrete Mathematics, 2nd ed. Reading, MA: Addison-Wesley, 
               pp. 111-115, 1994.
%H A102048 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GreatestPrimeFactor.html">Link to a section of The World of Mathematics.</
               a>
%H A102048 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Factorial.html">Link to a section of The World of Mathematics.</a>
%H A102048 <a href="Sindx_Fa.html#factorial">Index entries for sequences related 
               to factorial numbers.</a>
%F A102048 1+Sum(k=1 to [log(n-1)/log(P)], [(n-1)/P^k]) for n>1, where P = A006530(n) 
               is the greatest prime factor of n.
%e A102048 a(6) = 2 because A046021(6) = 9 = 3^2 = A006530(6)^2.
%t A102048 With[{p=First[Last[FactorInteger[n, FactorComplete->True]]]}, 1+Sum[Floor[(n-1)/
               p^k], {k, Floor[Log[n-1]/Log[p]]}]]
%Y A102048 Cf. A046021, A006530.
%Y A102048 Sequence in context: A000001 A146002 A109087 this_sequence A102551 A152823 
               A086545
%Y A102048 Adjacent sequences: A102045 A102046 A102047 this_sequence A102049 A102050 
               A102051
%K A102048 nonn
%O A102048 1,4
%A A102048 Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Dec 26 2004

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