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A285801 Numbers having at most one odd prime factor to an odd power in their prime factorization.

%I A285801 #12 Dec 07 2019 13:03:27
%S A285801 1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,22,23,24,25,26,27,28,
%T A285801 29,31,32,34,36,37,38,40,41,43,44,45,46,47,48,49,50,52,53,54,56,58,59,
%U A285801 61,62,63,64,67,68,71,72,73,74,75,76,79,80,81,82,83,86,88,89
%N A285801 Numbers having at most one odd prime factor to an odd power in their prime factorization.
%C A285801 The sequence is of asymptotic density zero. It seems to grow faster than n*(log_10(n)-1), which is a fair approximation in the range 10^3 .. 10^6 or beyond, cf. examples.
%H A285801 N. J. A. Sloane, <a href="/A285801/b285801.txt">Table of n, a(n) for n = 1..10001</a>
%e A285801 A285800(1) = 15 = 3*5 is the smallest positive integer to have two odd prime factors to an odd power (here 1) in its factorization, therefore it's the first number not in this sequence.
%e A285801 A285800(2) = 21 = 3*7, A285800(3) = 30 = 2*A285800(1) and A285800(3) = 33 = 3*11 are the next three numbers not in this sequence.
%e A285801 a(10) = 10, a(100) = 137, a(10^3) = 2066, a(10^4) = 29996, a(10^5) = 402878, a(10^6) = 5083823.
%p A285801 s800:=[]; s801:=[1];
%p A285801 for n from 2 to 1000 do
%p A285801 c:=0;
%p A285801 t2:=ifactors(n)[2];
%p A285801 for t3 in t2 do if t3[1]>2 and (t3[2] mod 2 = 1) then c:=c+1; fi; od:
%p A285801 if c <= 1 then s801:=[op(s801),n]; else s800:=[op(s800),n]; fi;
%p A285801 od:
%p A285801 s800; # A285800
%p A285801 s801; # A285801 - _N. J. A. Sloane_, Sep 30 2017
%o A285801 (PARI) is(n)=2>#select(t->bittest(t,0),factor(n>>valuation(n,2))[,2])
%Y A285801 Complement of A285800.
%K A285801 nonn,easy
%O A285801 1,2
%A A285801 _M. F. Hasler_, Apr 26 2017