cp's OEIS Frontend

A362333 Least nonnegative integer k such that (gpf(n)!)^k is divisible by n, where gpf(n) is the greatest prime factor of n.

%I A362333 #8 Mar 22 2024 09:17:11
%S A362333 0,1,1,2,1,1,1,3,2,1,1,2,1,1,1,4,1,2,1,1,1,1,1,3,2,1,3,1,1,1,1,5,1,1,
%T A362333 1,2,1,1,1,1,1,1,1,1,2,1,1,4,2,2,1,1,1,3,1,1,1,1,1,1,1,1,1,6,1,1,1,1,
%U A362333 1,1,1,3,1,1,2,1,1,1,1,2,4,1,1,1,1,1,1
%N A362333 Least nonnegative integer k such that (gpf(n)!)^k is divisible by n, where gpf(n) is the greatest prime factor of n.
%C A362333 First differs from A088388 at n = 40.
%F A362333 a(n) > 1 if and only if n is in A057109.
%F A362333 a(n) <= A051903(n).
%F A362333 a(n) = ceiling(A371148(n)/A371149(n)). - _Pontus von Brömssen_, Mar 16 2024
%e A362333 For n = 12, gpf(n)! = 3! = 6 is not divisible by 12, but (3!)^2 = 36 is divisible by 12, so a(12) = 2.
%o A362333 (Python)
%o A362333 from sympy import factorint
%o A362333 def A362333(n):
%o A362333     f = factorint(n)
%o A362333     gpf = max(f,default=None)
%o A362333     a = 0
%o A362333     for p in f:
%o A362333         m = gpf
%o A362333         v = 0
%o A362333         while m >= p:
%o A362333             m //= p
%o A362333             v += m
%o A362333         a = max(a,-(-f[p]//v))
%o A362333     return a
%Y A362333 Cf. A006530, A051903, A057109, A088388, A371148, A371149, A371151, A371152.
%K A362333 nonn
%O A362333 1,4
%A A362333 _Pontus von Brömssen_, Apr 16 2023