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

Author

R. J. Mathar, Oct 02 2012

Keywords

• nonn
• easy

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

All prime powers (A000961) are fixed points.

Examples

			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.
		

Links

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

Crossrefs

Used in A124833.

Cf. A000961, A006530, A007947.

Programs

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) ;

PARI

a(n) = my(f=factor(n)); for (k=1, #f~-1, f[k,2]--); factorback(f); \\ Michel Marcus, Jun 28 2021

Formula

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

Extensions

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

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