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A381404 a(n) is the mode of the multiset of bases and exponents (including exponents = 1) in the prime factorization of n (using largest mode if multimodal).

%I A381404 #7 Mar 01 2025 12:19:27
%S A381404 2,3,2,5,1,7,3,3,1,11,2,13,1,1,4,17,2,19,2,1,1,23,3,5,1,3,2,29,1,31,5,
%T A381404 1,1,1,2,37,1,1,5,41,1,43,2,5,1,47,4,7,2,1,2,53,3,1,7,1,1,59,2,61,1,7,
%U A381404 6,1,1,67,2,1,1,71,3,73,1,5,2,1,1,79,5,4,1,83,2,1,1
%N A381404 a(n) is the mode of the multiset of bases and exponents (including exponents = 1) in the prime factorization of n (using largest mode if multimodal).
%H A381404 Paolo Xausa, <a href="/A381404/b381404.txt">Table of n, a(n) for n = 2..10000</a>
%F A381404 a(p) = p, for p prime.
%e A381404 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 largest most frequent element is 2.
%t A381404 A381404[n_] := Max[Commonest[Flatten[FactorInteger[n]]]];
%t A381404 Array[A381404, 100, 2]
%Y A381404 Cf. A035306, A381178, A381403.
%Y A381404 Cf. A000040 (fixed points).
%K A381404 nonn,easy
%O A381404 2,1
%A A381404 _Paolo Xausa_, Feb 27 2025