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A381403 a(n) is the mode of the multiset of bases and exponents (including exponents = 1) in the prime factorization of n (using smallest mode if multimodal).

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%I A381403 #8 Mar 01 2025 12:19:17
%S A381403 1,1,2,1,1,1,2,2,1,1,2,1,1,1,2,1,2,1,2,1,1,1,3,2,1,3,2,1,1,1,2,1,1,1,
%T A381403 2,1,1,1,1,1,1,1,2,1,1,1,1,2,2,1,2,1,3,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,
%U A381403 1,1,2,1,1,1,2,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1
%N A381403 a(n) is the mode of the multiset of bases and exponents (including exponents = 1) in the prime factorization of n (using smallest mode if multimodal).
%H A381403 Paolo Xausa, <a href="/A381403/b381403.txt">Table of n, a(n) for n = 2..10000</a>
%F A381403 a(p) = 1, for p prime.
%e A381403 The prime factorization of 132 is 2^2*3^1*11^1, the multiset of these bases and exponents is {1, 1, 2, 2, 3, 11} and its smallest most frequent element is 1.
%t A381403 A381403[n_] := Min[Commonest[Flatten[FactorInteger[n]]]];
%t A381403 Array[A381403, 100, 2]
%Y A381403 Cf. A035306, A381178, A381404.
%K A381403 nonn,easy
%O A381403 2,3
%A A381403 _Paolo Xausa_, Feb 27 2025