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Numbers whose maximum exponent in their prime factorization is a powerful number larger than 1.
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%I #10 Jul 14 2024 08:52:55

%S 16,48,80,81,112,144,162,176,208,240,256,272,304,324,336,368,400,405,

%T 432,464,496,512,528,560,567,592,624,625,648,656,688,720,752,768,784,

%U 810,816,848,880,891,912,944,976,1008,1040,1053,1072,1104,1134,1136,1168,1200

%N Numbers whose maximum exponent in their prime factorization is a powerful number larger than 1.

%C Subsequence of A130897 and first differs from it at n = 115: A130897(115) = 2592 = 2^5 * 3^4 is not a term of this sequence.

%C The asymptotic density of this sequence is d = Sum_{k > 1 and in A001694} (1/zeta(k+1) - 1/zeta(k)) = 0.043523813088759413253... . The asymptotic density of this sequence within A130897 is d/(1 - A262276) = 0.98744988886705430331... .

%H Amiram Eldar, <a href="/A374589/b374589.txt">Table of n, a(n) for n = 1..10000</a>

%t powQ[n_] := Min[FactorInteger[n][[;; , 2]]] > 1; q[n_] := powQ[Max[ FactorInteger[n][[;; , 2]] ]]; Select[Range[1200], q]

%o (PARI) ispow(n) = n > 1 && ispowerful(n);

%o is(n) = n > 1 && ispow(vecmax(factor(n)[, 2]))

%Y Cf. A001694, A051903, A262276, A361177.

%Y Subsequence of A013929, A130897 and A372405.

%Y Similar sequences: A368714, A369937, A369938, A369939, A374588, A374590.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Jul 12 2024