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%I #15 Jul 17 2023 10:44:37
%S 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 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 2,7,2,5,2,67,17,3,2,71,3,73,2,3,19,7,2,79,5
%N Smallest prime factor with minimal exponent in canonical prime factorization of n, a(1)=1.
%H Alois P. Heinz, <a href="/A067695/b067695.txt">Table of n, a(n) for n = 1..20000</a>
%e a(12) = a(2^2 * 3^1) = 3, but A020639(12) = 2;
%e a(36) = a(2^2 * 3^2) = 2 = A020639(36).
%p a:= n-> `if`(n=1, 1, (l-> (m-> min(map(i-> i[1], select(y->
%p y[2]=m, l))))(min(map(x-> x[2], l))))(ifactors(n)[2])):
%p seq(a(n), n=1..80); # _Alois P. Heinz_, Jan 25 2023
%o (Python)
%o from sympy import factorint
%o def A067695(n):
%o if n == 1: return 1
%o f, g = map(tuple,zip(*sorted(factorint(n).items())))
%o return f[g.index(min(g))] # _Chai Wah Wu_, Feb 07 2023
%o (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 Cf. A020639, A034684, A028233, A051904, A067029.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Feb 23 2002
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