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A381201 a(n) is the product of the elements of the set of bases and exponents in the prime factorization of n.

%I A381201 #14 Feb 18 2025 18:57:06
%S A381201 1,2,3,2,5,6,7,6,6,10,11,6,13,14,15,8,17,6,19,10,21,22,23,6,10,26,3,
%T A381201 14,29,30,31,10,33,34,35,6,37,38,39,30,41,42,43,22,30,46,47,24,14,10,
%U A381201 51,26,53,6,55,42,57,58,59,30,61,62,42,12,65,66,67,34,69,70
%N A381201 a(n) is the product of the elements of the set of bases and exponents in the prime factorization of n.
%C A381201 The prime factorization of 1 is the empty set, so a(1) = 1 by convention (empty product).
%H A381201 Paolo Xausa, <a href="/A381201/b381201.txt">Table of n, a(n) for n = 1..10000</a>
%e A381201 a(12) = 6 because 12 = 2^2*3^1, the set of these bases and exponents is {1, 2, 3} and 1*2*3 = 6.
%e A381201 a(31500) = 210 because 31500 = 2^2*3^2*5^3*7^1, the set of these bases and exponents is {1, 2, 3, 5, 7} and 1*2*3*5*7 = 210.
%t A381201 A381201[n_] := Times @@ Union[Flatten[FactorInteger[n]]];
%t A381201 Array[A381201, 100]
%o A381201 (PARI) a(n) = my(f=factor(n)); vecprod(Vec(setunion(Set(f[,1]), Set(f[,2])))); \\ _Michel Marcus_, Feb 18 2025
%Y A381201 Cf. A000026, A336965, A381202, A381203, A381204, A381205.
%K A381201 nonn,easy
%O A381201 1,2
%A A381201 _Paolo Xausa_, Feb 16 2025