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A359612 Largest prime factor with minimal exponent in canonical prime factorization of n.

%I A359612 #30 Feb 08 2023 10:10:23
%S A359612 2,3,2,5,3,7,2,3,5,11,3,13,7,5,2,17,2,19,5,7,11,23,3,5,13,3,7,29,5,31,
%T A359612 2,11,17,7,3,37,19,13,5,41,7,43,11,5,23,47,3,7,2,17,13,53,2,11,7,19,
%U A359612 29,59,5,61,31,7,2,13,11,67,17,23,7,71,3,73,37,3
%N A359612 Largest prime factor with minimal exponent in canonical prime factorization of n.
%C A359612 When inspecting the minimal exponent of the canonical representation of n, a(n) is the largest of those primes, while A067695(n) is the smallest.
%C A359612 On the other hand if the maximal exponent is regarded similarly, A356840(n) is the largest of those primes and A356838(n) is the smallest.
%C A359612 18 is the smallest n, where a(n) differs from A006530(n), since a(18) = 2, while A006530(18) = 3.
%H A359612 Alois P. Heinz, <a href="/A359612/b359612.txt">Table of n, a(n) for n = 2..20000</a>
%e A359612 a(162) = a(2^1 * 3^4) = 2.
%e A359612 a(225) = a(3^2 * 5^2) = 5.
%p A359612 a:= n-> (l-> (m-> max(map(i-> i[1], select(y->y[2]=m,
%p A359612          l))))(min(map(x-> x[2], l))))(ifactors(n)[2]):
%p A359612 seq(a(n), n=2..75);  # _Alois P. Heinz_, Jan 25 2023
%t A359612 a[n_] := Module[{f = FactorInteger[n], e, ind}, e = f[[;; , 2]]; ind = Position[e, Min[e]][[-1, 1]]; f[[ind, 1]]]; Array[a, 100, 2] (* _Amiram Eldar_, Jan 07 2023 *)
%o A359612 (Python)
%o A359612 from sympy import factorint
%o A359612 def a(n):
%o A359612     max_factor = 0
%o A359612     min_exponent = float("inf")
%o A359612     for p, exponent in factorint(n).items():
%o A359612         if exponent < min_exponent:
%o A359612             max_factor = p
%o A359612             min_exponent = exponent
%o A359612         elif exponent == min_exponent:
%o A359612             max_factor = max(max_factor, p)
%o A359612     return max_factor
%o A359612 (Python)
%o A359612 from sympy import factorint
%o A359612 def A359612(n): return (f:=list(map(tuple,zip(*sorted(factorint(n).items(),reverse=True)))))[0][f[1].index(min(f[1]))] # _Chai Wah Wu_, Feb 07 2023
%o A359612 (PARI) a(n) = my(f=factor(n), e=vecmin(f[,2])); f[vecmax(select(x->(x==e), f[,2], 1)), 1]; \\ _Michel Marcus_, Jan 26 2023
%Y A359612 Cf. A006530, A067695, A356838, A356840.
%K A359612 nonn
%O A359612 2,1
%A A359612 _Jens Ahlström_, Jan 06 2023