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%I #8 Mar 22 2024 09:17:11
%S 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 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 1,1,1,3,1,1,2,1,1,1,1,2,4,1,1,1,1,1,1
%N Least nonnegative integer k such that (gpf(n)!)^k is divisible by n, where gpf(n) is the greatest prime factor of n.
%C First differs from A088388 at n = 40.
%F a(n) > 1 if and only if n is in A057109.
%F a(n) <= A051903(n).
%F a(n) = ceiling(A371148(n)/A371149(n)). - _Pontus von Brömssen_, Mar 16 2024
%e 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 (Python)
%o from sympy import factorint
%o def A362333(n):
%o f = factorint(n)
%o gpf = max(f,default=None)
%o a = 0
%o for p in f:
%o m = gpf
%o v = 0
%o while m >= p:
%o m //= p
%o v += m
%o a = max(a,-(-f[p]//v))
%o return a
%Y Cf. A006530, A051903, A057109, A088388, A371148, A371149, A371151, A371152.
%K nonn
%O 1,4
%A _Pontus von Brömssen_, Apr 16 2023