login
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, 71
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_1-1) *p_2^(e_2-1) *... *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
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) ;
PROG
(PARI) a(n) = my(f=factor(n)); for (k=1, #f~-1, f[k, 2]--); factorback(f); \\ Michel Marcus, Jun 28 2021
CROSSREFS
Used in A124833.
Sequence in context: A327393 A376368 A376664 * A322035 A325943 A295126
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Oct 02 2012
EXTENSIONS
a(71) corrected by Georg Fischer, Jun 28 2021
STATUS
approved