

A056813


Largest nonunitary prime factor of LCM(1,...,n); that is, the largest prime which occurs to power > 1 in prime factorization of LCM(1,..,n).


3



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, 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, 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
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OFFSET

1,4


COMMENTS

For n>0, prime(n) appears {(prime(n+1))^2  (prime(n))^2} times [from n=(prime(n))^2 to n=(prime(n+1))^2  1], that is, A000040(n) appears A069482(n) times (from n=A001248(n) to n=A084920(n+1)).  Lekraj Beedassy, Mar 31 2005
a(n) is the largest prime factor of A045948(n). [Matthew Vandermast, Oct 29 2008]
Alternative definition: a(n) = largest prime <= sqrt(n) (considering 1 as prime for this occasion, see A008578 for the 19th century definition of primes).  JeanChristophe Hervé, Oct 29 2013


LINKS

JeanChristophe Hervé, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = prime(w) if prime(w)^2 <= n < prime(w+1)^2.
To get the sequence, repeat 1 three times, and then for any k >= 1, repeat A000040(k) A069482(k) times; or equivalently, for any k >= 1, repeat A008578(k) a number of times equal to A008578(k+1)^2  A008578(k)^2.  JeanChristophe Hervé, Oct 29 2013


EXAMPLE

The jth prime appears at the position of its square, at n = prime(j)^2.


MATHEMATICA

Table[f = Transpose[FactorInteger[LCM @@ Range[n]]]; pos = Position[f[[2]], _?(# > 1 &)]; If[pos == {}, 1, f[[1, pos[[1]]]][[1]]], {n, 100}] (* T. D. Noe, Oct 30 2013 *)


CROSSREFS

Cf. A054041, A056170.
Cf. A000040, A001248, A008578, A069482.
Sequence in context: A343437 A105517 A230774 * A125269 A077430 A105513
Adjacent sequences: A056810 A056811 A056812 * A056814 A056815 A056816


KEYWORD

nonn,easy


AUTHOR

Labos Elemer, Aug 28 2000


EXTENSIONS

Corrected offset by JeanChristophe Hervé, Oct 29 2013


STATUS

approved



