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

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, 29, 31, 32, 34, 36, 37, 38, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 56, 58, 59, 61, 62, 63, 64, 67, 68, 71, 72, 73, 74, 75, 76, 79, 80, 81, 82, 83, 86, 88, 89

Offset: 1

Author

M. F. Hasler, Apr 26 2017

Keywords

• nonn
• easy

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.

Examples

			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.
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..10001

Crossrefs

Complement of A285800.

Programs

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

PARI

is(n)=2>#select(t->bittest(t,0),factor(n>>valuation(n,2))[,2])