A217434 n divided by the product of all its prime divisors smaller than the largest prime divisor.

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

Michel Marcus, Table of n, a(n) for n = 1..10000

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.

Cf. A000961, A006530, A007947.

Sequence in context: A327393 A376368 A376664 * A322035 A325943 A295126

Adjacent sequences: A217431 A217432 A217433 * A217435 A217436 A217437

Keyword

nonn,easy

Author

R. J. Mathar, Oct 02 2012

Extensions

a(71) corrected by Georg Fischer, Jun 28 2021

Status

approved