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Numbers whose maximum exponent in their prime factorization is an evil number (A001969).
5

%I #10 Jul 14 2024 08:53:05

%S 8,24,27,32,40,54,56,64,72,88,96,104,108,120,125,135,136,152,160,168,

%T 184,189,192,200,216,224,232,243,248,250,264,270,280,288,296,297,312,

%U 320,328,343,344,351,352,360,375,376,378,392,408,416,424,440,448,456,459

%N Numbers whose maximum exponent in their prime factorization is an evil number (A001969).

%C The asymptotic density of this sequence is Sum_{k in A001969} (1/zeta(k+1) - 1/zeta(k)) = 0.12101890210392912747... .

%H Amiram Eldar, <a href="/A374590/b374590.txt">Table of n, a(n) for n = 1..10000</a>

%t evilQ[n_] := EvenQ[DigitCount[n, 2, 1]]; q[n_] := evilQ[Max[FactorInteger[n][[;; , 2]]]]; Select[Range[500], q]

%o (PARI) is(n) = n > 1 && !(hammingweight(vecmax(factor(n)[, 2])) % 2);

%Y Cf. A001969, A051903.

%Y Subsequence of A013929 and A262675 \ {1}.

%Y Similar sequences: A368714, A369937, A369938, A369939, A374588, A374589.

%K nonn,easy,base

%O 1,1

%A _Amiram Eldar_, Jul 12 2024