

A217434


n divided by the product of all its prime divisors smaller than the largest prime divisor.


1



1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 6, 13, 7, 5, 16, 17, 9, 19, 10, 7, 11, 23, 12, 25, 13, 27, 14, 29, 5, 31, 32, 11, 17, 7, 18, 37, 19, 13, 20, 41, 7, 43, 22, 15, 23, 47, 24, 49, 25, 17, 26, 53, 27, 11, 28, 19, 29, 59, 10, 61, 31, 21, 64, 13, 11, 67, 34, 23, 7, 7
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OFFSET

1,2


COMMENTS

If n = p_1^e_1 *p_2^e_2 *p_3^e_3 *...* p_m^e_m is the canonical prime factorization of n with e_1, e_2, e_3,.. >0 and p_1<p_2<p_3<...<p_m, then a(n) = p_1^(e_11) *p_2^(e_21) *... *p_m^e^m, where exponents of all prime factors are decremented by 1, with the exception of the exponent associated with the largest prime prime factor that stays intact.
All prime powers (A000961) are fixed points.


LINKS

Table of n, a(n) for n=1..71.


FORMULA

a(n) = n*A006530(n)/A007947(n).


EXAMPLE

For n=24 = 2^3*3, the exponent 3 (associated with the smaller prime 2) is reduced to 2, so a(n)=2^2*3=12.


MAPLE

A217434 := proc(n)
local s, m, a, p ;
s := numtheory[factorset](n) ;
m := max(op(s)) ;
a := n ;
for p in s do
if p < m then
a := a/p ;
end if;
end do:
a ;
end proc:
seq(A217434(n), n=1..100) ;


CROSSREFS

Used in A124833.
Sequence in context: A098988 A274346 A034699 * A295126 A235602 A111615
Adjacent sequences: A217431 A217432 A217433 * A217435 A217436 A217437


KEYWORD

nonn,easy


AUTHOR

R. J. Mathar, Oct 02 2012


STATUS

approved



