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A381951 Nonsquarefree odd numbers whose prime factorization has an odd maximum exponent.

%I A381951 #7 Mar 12 2025 08:24:16
%S A381951 27,125,135,189,243,297,343,351,375,459,513,621,675,783,837,875,945,
%T A381951 999,1029,1107,1125,1161,1215,1269,1323,1331,1375,1431,1485,1593,1625,
%U A381951 1647,1701,1715,1755,1809,1917,1971,2079,2125,2133,2187,2197,2241,2295,2375,2403,2457
%N A381951 Nonsquarefree odd numbers whose prime factorization has an odd maximum exponent.
%C A381951 Nonsquarefree odd numbers k such that A051903(k) is odd, or equivalently, odd numbers k such that A051903(k) is an odd number that is larger than 1.
%C A381951 The asymptotic density of this sequence is (1/2) * Sum_{k>=3} (-1)^(k+1) * (1 - 2^k/((2^k-1)*zeta(k))) = 0.019098071299657074975... .
%H A381951 Amiram Eldar, <a href="/A381951/b381951.txt">Table of n, a(n) for n = 1..10000</a>
%e A381951 125 = 5^3 is a term since it is odd, divisible by a square (25, and thus it is nonsquarefree), and the maximum exponent in its prime factorization is 3, which is odd.
%t A381951 q[n_] := n > 1 && OddQ[n]; Select[Range[1, 2500, 2], q[Max[FactorInteger[#][[;; , 2]]]] &]
%o A381951 (PARI) isok(k) = k > 1 && k % 2 && apply(x -> (x > 1 && x % 2), vecmax(factor(k)[, 2]));
%Y A381951 Intersection of A005408 and A376142.
%Y A381951 Complement of A381950 within A013929.
%Y A381951 Cf. A051903.
%K A381951 nonn,easy
%O A381951 1,1
%A A381951 _Amiram Eldar_, Mar 11 2025