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 A056813 Largest non-unitary prime factor of LCM[1,...,n]; i.e. the largest prime which occurs to power > 1 in prime factorization of LCM[1,..,n]. 0

%I

%S 1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,

%T 5,5,5,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,

%U 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7

%N Largest non-unitary prime factor of LCM[1,...,n]; i.e. the largest prime which occurs to power > 1 in prime factorization of LCM[1,..,n].

%C For n>0, p(n) appears {(p(n+1))^2 - (p(n))^2} times [from n=(p(n))^2 to n=(p(n+1))^2 - 1], i.e., A000040(n) appears A069482(n) times[from n=A001248(n) to n=A084920(n+1)] - _Lekraj Beedassy_, Mar 31 2005

%C a(n) is the largest prime factor of A045948(n). [From _Matthew Vandermast_, Oct 29 2008]

%F a(n)=p(w) if p(w)^2 <= n < p(w+1)^2.

%e The j-th prime appears at the position of its square, at n=P(j)^2.

%Y Cf. A054041, A056170.

%K nonn

%O 0,4

%A Labos E. (labos(AT)ana.sote.hu), Aug 28 2000

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