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A285800 Numbers having more than one odd prime factor to an odd power in their prime factorization.

%I A285800 #17 Oct 01 2023 01:57:35
%S A285800 15,21,30,33,35,39,42,51,55,57,60,65,66,69,70,77,78,84,85,87,91,93,95,
%T A285800 102,105,110,111,114,115,119,120,123,129,130,132,133,135,138,140,141,
%U A285800 143,145,154,155,156,159,161,165,168,170,174,177,182,183,185,186
%N A285800 Numbers having more than one odd prime factor to an odd power in their prime factorization.
%C A285800 The sequence is of asymptotic density one, a(n) ~ n.
%H A285800 N. J. A. Sloane, <a href="/A285800/b285800.txt">Table of n, a(n) for n = 1..19999</a>
%e A285800 15 = 3*5, 21 = 3*7, 30 = 2*15, 33 = 3*11 are the smallest positive integers having at least two prime factors to an odd power in their factorization.
%e A285800 a(10) = 57, a(100) = 287, a(10^3) = 1950, a(10^4) = 15701, a(10^5) = 138540, a(10^6) = 1284998.
%p A285800 s800:=[]; s801:=[1];
%p A285800 for n from 2 to 1000 do
%p A285800 c:=0;
%p A285800 t2:=ifactors(n)[2];
%p A285800 for t3 in t2 do if t3[1]>2 and (t3[2] mod 2 = 1) then c:=c+1; fi; od:
%p A285800 if c <= 1 then s801:=[op(s801),n]; else s800:=[op(s800),n]; fi;
%p A285800 od:
%p A285800 s800; # A285800
%p A285800 s801; # A285801 - _N. J. A. Sloane_, Sep 30 2017
%o A285800 (PARI) is(n)=1<#select(t->bittest(t,0),factor(n>>valuation(n,2))[,2])
%Y A285800 Subsequence of A248150.
%Y A285800 Complement of A285801.
%K A285800 nonn,easy
%O A285800 1,1
%A A285800 _M. F. Hasler_, Apr 26 2017