OFFSET
1,2
COMMENTS
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.
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..10001
EXAMPLE
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.
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.
a(10) = 10, a(100) = 137, a(10^3) = 2066, a(10^4) = 29996, a(10^5) = 402878, a(10^6) = 5083823.
MAPLE
s800:=[]; s801:=[1];
for n from 2 to 1000 do
c:=0;
t2:=ifactors(n)[2];
for t3 in t2 do if t3[1]>2 and (t3[2] mod 2 = 1) then c:=c+1; fi; od:
if c <= 1 then s801:=[op(s801), n]; else s800:=[op(s800), n]; fi;
od:
s800; # A285800
s801; # A285801 - N. J. A. Sloane, Sep 30 2017
PROG
(PARI) is(n)=2>#select(t->bittest(t, 0), factor(n>>valuation(n, 2))[, 2])
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Apr 26 2017
STATUS
approved