A038109 Divisible exactly by the square of a prime.

4, 9, 12, 18, 20, 25, 28, 36, 44, 45, 49, 50, 52, 60, 63, 68, 72, 75, 76, 84, 90, 92, 98, 99, 100, 108, 116, 117, 121, 124, 126, 132, 140, 144, 147, 148, 150, 153, 156, 164, 169, 171, 172, 175, 180, 188, 196, 198, 200, 204, 207, 212, 220, 225, 228, 234, 236, 242

Offset: 1

Author

Felice Russo

Keywords

• nonn
• easy

Comments

Numbers for which at least one prime factor exponent is exactly 2.

Sometimes called squarefull numbers, although that term is usually reserved for A001694. - N. J. A. Sloane, Jul 22 2012

The asymptotic density of this sequence is 1 - A330596 = 0.2514647... - Amiram Eldar, Aug 12 2020

Examples

			20=5*2*2 is divisible by 2^2.
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1247

Crossrefs

Cf. A001694, A013929, A284017, A284018.

Programs

Maple

isA038109 := proc(n)
    local p;
    for p in ifactors(n)[2] do
        if op(2,p) = 2 then
            return true;
        end if;
    end do:
    false ;
end proc: # R. J. Mathar, Dec 08 2015
# second Maple program:
q:= n-> ormap(i-> i[2]=2, ifactors(n)[2]):
select(q, [$1..300])[];  # Alois P. Heinz, Aug 12 2020

Mathematica

Select[Range[250],MemberQ[Transpose[FactorInteger[#]][[2]],2]&] (* Harvey P. Dale, Sep 24 2012 *)

PARI

is(n)=#select(n->n==2, Set(factor(n)[,2])) \\ Charles R Greathouse IV, Sep 17 2015

Extensions

Corrected and extended by Erich Friedman