

A105562


a(n) is the prime whose index is the greatest prime factor of n, for n >1; a(1)=2.


2



2, 3, 5, 3, 11, 5, 17, 3, 5, 11, 31, 5, 41, 17, 11, 3, 59, 5, 67, 11, 17, 31, 83, 5, 11, 41, 5, 17, 109, 11, 127, 3, 31, 59, 17, 5, 157, 67, 41, 11, 179, 17, 191, 31, 11, 83, 211, 5, 17, 11, 59, 41, 241, 5, 31, 17, 67, 109, 277, 11, 283, 127, 17, 3, 41, 31, 331, 59, 83, 17, 353, 5
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OFFSET

1,1


COMMENTS

Previous name: a(n) is the kth prime number, where k is the greatest prime number dividing n, a(1) = 2.
If n is in standard form, that is, n = p_1^n_1 * p_2^n_2 * ... * p_k^n_k where p_1, p_2, ..., p_k are primes with p_1 < p_2 <...< p_k and n_1 > 0, n_2 > 0, ..., n_k > 0 then a(n) = prime(p_k) = A000040(p_k).  Muniru A Asiru, Nov 26 2018


LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A000040(A006530(n)).


EXAMPLE

From Muniru A Asiru, Nov 26 2018: (Start)
For n = 6, the greatest prime number dividing 6 is 3. Hence, a(6) = prime(3) = 5.
For n = 7, the greatest prime number dividing 7 is 7. Therefore, a(7) = prime(7) = 17.
For n = 666 = 2*3^2*37, the greatest prime number dividing 666 is 37. Hence, a(666) = prime(37) = 157. (End)


MAPLE

a:= n> ithprime(max(1, seq(i[1], i=ifactors(n)[2]))):
seq(a(n), n=1..80); # Alois P. Heinz, Nov 28 2018


MATHEMATICA

Prime[FactorInteger[#][[1, 1]]] & /@ Range[2, 75] (* Harvey P. Dale, Apr 11 2011 *)


PROG

(PARI) a(n) = if (n==1, 2, prime(vecmax(factor(n)[, 1]))); \\ Michel Marcus, Nov 26 2018
(GAP) P:=Filtered([1..300], IsPrime);; a:=List(List([1..65], n>Reversed(Factors(n))), i>P[i[1]]); # Muniru A Asiru, Nov 26 2018


CROSSREFS

Cf. A000040, A006530, A105574.
Sequence in context: A211245 A107473 A105574 * A323704 A272202 A244609
Adjacent sequences: A105559 A105560 A105561 * A105563 A105564 A105565


KEYWORD

easy,nonn,less


AUTHOR

Cino Hilliard, May 03 2005


EXTENSIONS

a(1)=2 prepended by Muniru A Asiru, Nov 26 2018
New name from Michel Marcus, Dec 09 2018


STATUS

approved



