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A067695 Smallest prime factor with minimum exponent in canonical prime factorization of n, a(1)=1.

%I A067695 #20 Sep 09 2024 02:40:49
%S A067695 1,2,3,2,5,2,7,2,3,2,11,3,13,2,3,2,17,2,19,5,3,2,23,3,5,2,3,7,29,2,31,
%T A067695 2,3,2,5,2,37,2,3,5,41,2,43,11,5,2,47,3,7,2,3,13,53,2,5,7,3,2,59,3,61,
%U A067695 2,7,2,5,2,67,17,3,2,71,3,73,2,3,19,7,2,79,5
%N A067695 Smallest prime factor with minimum exponent in canonical prime factorization of n, a(1)=1.
%H A067695 Alois P. Heinz, <a href="/A067695/b067695.txt">Table of n, a(n) for n = 1..20000</a>
%e A067695 a(12) = a(2^2 * 3^1) = 3, but A020639(12) = 2;
%e A067695 a(36) = a(2^2 * 3^2) = 2 = A020639(36).
%p A067695 a:= n-> `if`(n=1, 1, (l-> (m-> min(map(i-> i[1], select(y->
%p A067695       y[2]=m, l))))(min(map(x-> x[2], l))))(ifactors(n)[2])):
%p A067695 seq(a(n), n=1..80);  # _Alois P. Heinz_, Jan 25 2023
%t A067695 a[n_] := Module[{f = FactorInteger[n], p, e}, Min[Select[f, Last[#] == Min[f[[;;, 2]]] &][[;;, 1]]]]; a[1] = 1; Array[a, 100] (* _Amiram Eldar_, Sep 08 2024 *)
%o A067695 (Python)
%o A067695 from sympy import factorint
%o A067695 def A067695(n):
%o A067695     if n == 1: return 1
%o A067695     f, g = map(tuple,zip(*sorted(factorint(n).items())))
%o A067695     return f[g.index(min(g))] # _Chai Wah Wu_, Feb 07 2023
%o A067695 (PARI) a(n) = if (n==1, 1, my(f=factor(n), i=vecmin(f[,2])); f[vecmin(select(x->(x==i), f[,2], 1)), 1]); \\ _Michel Marcus_, Jul 17 2023
%Y A067695 Cf. A020639, A034684, A028233, A051904, A067029.
%K A067695 nonn
%O A067695 1,2
%A A067695 _Reinhard Zumkeller_, Feb 23 2002