|
%I #14 Jun 29 2021 11:20:49
%S 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,
%T 29,5,31,32,11,17,7,18,37,19,13,20,41,7,43,22,15,23,47,24,49,25,17,26,
%U 53,27,11,28,19,29,59,10,61,31,21,64,13,11,67,34,23,7,71
%N n divided by the product of all its prime divisors smaller than the largest prime divisor.
%C 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.
%C All prime powers (A000961) are fixed points.
%H Michel Marcus, <a href="/A217434/b217434.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = n*A006530(n)/A007947(n).
%e 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.
%p A217434 := proc(n)
%p local s,m,a,p ;
%p s := numtheory[factorset](n) ;
%p m := max(op(s)) ;
%p a := n ;
%p for p in s do
%p if p < m then
%p a := a/p ;
%p end if;
%p end do:
%p a ;
%p end proc:
%p seq(A217434(n),n=1..100) ;
%o (PARI) a(n) = my(f=factor(n)); for (k=1, #f~-1, f[k,2]--); factorback(f); \\ _Michel Marcus_, Jun 28 2021
%Y Used in A124833.
%Y Cf. A000961, A006530, A007947.
%K nonn,easy
%O 1,2
%A _R. J. Mathar_, Oct 02 2012
%E a(71) corrected by _Georg Fischer_, Jun 28 2021
|
