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

15, 21, 30, 33, 35, 39, 42, 51, 55, 57, 60, 65, 66, 69, 70, 77, 78, 84, 85, 87, 91, 93, 95, 102, 105, 110, 111, 114, 115, 119, 120, 123, 129, 130, 132, 133, 135, 138, 140, 141, 143, 145, 154, 155, 156, 159, 161, 165, 168, 170, 174, 177, 182, 183, 185, 186

Offset: 1

Author

M. F. Hasler, Apr 26 2017

Keywords

• nonn
• easy

Comments

The sequence is of asymptotic density one, a(n) ~ n.

Examples

			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.
a(10) = 57, a(100) = 287, a(10^3) = 1950, a(10^4) = 15701, a(10^5) = 138540, a(10^6) = 1284998.
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..19999

Crossrefs

Subsequence of A248150.

Complement of A285801.

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)=1<#select(t->bittest(t,0),factor(n>>valuation(n,2))[,2])