

A038109


Divisible exactly by the square of a prime.


12



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
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OFFSET

1,1


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


LINKS

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


EXAMPLE

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


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 *)


PROG

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


CROSSREFS

Cf. A001694, A013929, A284017, A284018.
Sequence in context: A081619 A336594 A304365 * A067259 A060687 A286228
Adjacent sequences: A038106 A038107 A038108 * A038110 A038111 A038112


KEYWORD

nonn,easy


AUTHOR

Felice Russo


EXTENSIONS

Corrected and extended by Erich Friedman


STATUS

approved



