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A360769 Odd numbers that are neither prime powers nor squarefree.

%I A360769 #21 Mar 04 2023 02:08:28
%S A360769 45,63,75,99,117,135,147,153,171,175,189,207,225,245,261,275,279,297,
%T A360769 315,325,333,351,363,369,375,387,405,423,425,441,459,475,477,495,507,
%U A360769 513,525,531,539,549,567,575,585,603,605,621,637,639,657,675,693,711,725,735,747,765,775,783,801,819,825
%N A360769 Odd numbers that are neither prime powers nor squarefree.
%C A360769 Odd numbers k such that A001222(k) > A001221(k) > 1.
%H A360769 Michael De Vlieger, <a href="/A360769/b360769.txt">Table of n, a(n) for n = 1..10000</a>
%H A360769 Michael De Vlieger, <a href="/A360769/a360769.png">2048 pixel square bitmap</a> of n = 1..4194304, read left to right, top to bottom, showing odd A126706(n) in black.
%F A360769 a(n) = { A005408 INTERSECT A126706 } = intersection of A005418, A013929, and A024619.
%p A360769 filter:= proc(n) local F;
%p A360769 F:= ifactors(n)[2];
%p A360769 nops(F)>1 and max(F[..,2]) > 1
%p A360769 end proc:
%p A360769 select(filter, [seq(i, i = 1 .. 1000, 2)]); # _Robert Israel_, Mar 01 2023
%t A360769 Select[Range[1, 825, 2], Nor[PrimePowerQ[#], SquareFreeQ[#]] &]
%o A360769 (PARI) isok(k) = (k%2) && !isprimepower(k) && !issquarefree(k); \\ _Michel Marcus_, Feb 28 2023
%o A360769 (Python)
%o A360769 from itertools import count, islice
%o A360769 from sympy import factorint
%o A360769 def A360769_gen(startvalue=1): # generator of terms >= startvalue
%o A360769     return filter(lambda n: sum(f:=factorint(n).values()) > len(f) > 1,count(max(startvalue+(startvalue&1^1),1),2))
%o A360769 A360769_list = list(islice(A360769_gen(),20)) # _Chai Wah Wu_, Mar 01 2023
%Y A360769 Cf. A001221, A001222, A005418, A013929, A024619, A126706.
%K A360769 nonn
%O A360769 1,1
%A A360769 _Michael De Vlieger_, Feb 28 2023