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A376173 Numbers whose prime factorization has an odd minimum exponent that is larger than 1.

%I A376173 #11 Sep 13 2024 11:58:39
%S A376173 8,27,32,125,128,216,243,343,432,512,648,864,1000,1331,1728,1944,2000,
%T A376173 2048,2187,2197,2744,3125,3375,3456,4000,4913,5000,5488,5832,6859,
%U A376173 6912,7776,8000,8192,9261,10125,10648,10976,12167,13824,15552,16000,16807,16875,17496
%N A376173 Numbers whose prime factorization has an odd minimum exponent that is larger than 1.
%C A376173 Numbers k such that A051904(k) is odd and larger than 1.
%C A376173 The minimum exponent in the prime factorization of 1 is considered to be A051904(1) = 0, and therefore 1 is not a term of this sequence.
%H A376173 Amiram Eldar, <a href="/A376173/b376173.txt">Table of n, a(n) for n = 1..10000</a>
%H A376173 <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.
%F A376173 Sum_{n>=1} 1/a(n) = -1 + Sum_{k>=2} (-1)^k * s(k) = 0.2379998147971880759099..., where s(k) = Product_{p prime} (1 + 1/(p^k*(p-1))).
%t A376173 seq[lim_] := Select[Union@ Flatten@ Table[i^2 * j^3, {j, 1, Surd[lim, 3]}, {i, 1, Sqrt[lim/j^3]}], # > 1 && OddQ[Min[FactorInteger[#][[;; , 2]]]] &]; seq[10000]
%o A376173 (PARI) is(k) = {my(f = factor(k), e = f[,2]); #e && (ispowerful(f) && vecmin(e) % 2);}
%Y A376173 Subsequence of A036966.
%Y A376173 Complement of A376172 within A001694.
%Y A376173 Subsequences: A030078, A062838 \ {1}.
%Y A376173 Cf. A051904.
%K A376173 nonn,easy
%O A376173 1,1
%A A376173 _Amiram Eldar_, Sep 13 2024