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%I #8 May 21 2023 12:56:05
%S 25,121,225,343,1089,1323,2187,2197,3025,3087,3249,5929,6125,6859,
%T 7803,8575,9261,10125,11881,11907,14161,15125,16641,16807,19683,19773,
%U 21025,22707,25921,27889,29241,29791,30375,33275,36125,41067,42849,44217,45125,45369,49729
%N Odd powerful numbers (A062739) k such that the next powerful number after k is also odd.
%C A076445 is a subsequence if there are no three consecutive integers that are powerful numbers (A001694).
%H Amiram Eldar, <a href="/A363190/b363190.txt">Table of n, a(n) for n = 1..10000</a>
%e 25 = 5^2 is a term since it is an odd powerful number and the next powerful number, 27 = 3^3, is also odd.
%t With[{pow = Select[Range[10^5], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]}, pow[[Select[Range[Length[pow] - 1], OddQ[pow[[#]]] && OddQ[pow[[#+1]]] &]]]]
%o (PARI) lista(kmax) = {my(c = 0); for(k = 1, kmax, if(ispowerful(k), c++; if(k%2, print1(c, ", ")))); }
%Y Cf. A001694, A062739, A076445, A363189, A363191, A363192.
%K nonn,easy
%O 1,1
%A _Amiram Eldar_, May 21 2023
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