A082295 Numbers having more than two square divisors > 1.

36, 64, 72, 100, 108, 128, 144, 180, 192, 196, 200, 216, 225, 252, 256, 288, 300, 320, 324, 360, 384, 392, 396, 400, 432, 441, 448, 450, 468, 484, 500, 504, 512, 540, 576, 588, 600, 612, 640, 648, 675, 676, 684, 700, 704, 720, 729, 756, 768, 784, 792, 800

Offset

1,1

Comments

If n is in the sequence, so is m*n. - Charles R Greathouse IV, Oct 16 2015

The asymptotic density of this sequence is 1 - (6/Pi^2) * (1 + Sum_{p prime} (1/p^2 + 1/(p^3*(p+1)) + 1/(p^4*(p+1)))) = 0.07033321843992718294... . - Amiram Eldar, Sep 25 2022

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

A046951(a(n)) > 3.

a(n) < 17n for n > 25. - Charles R Greathouse IV, Oct 16 2015

Example

n=200 has 4 square divisors: 1, 4, 25 and 100, therefore 200 is a term.

Mathematica

Select[Range[1000], Length[Rest[Select[ Divisors[#], IntegerQ[ Sqrt[ #]]&]]]> 2&] (* Harvey P. Dale, Jan 08 2014 *)

Prog

(PARI) is(n)=my(f=vecsort(factor(n)[, 2], , 4)); #f && (f[1]>5 || (#f>1 && f[2]>1)) \\ Charles R Greathouse IV, Oct 16 2015

Crossrefs

Cf. A082294, A048111, A046951.

Sequence in context: A043242 A044022 A337862 * A343293 A326666 A272190

Adjacent sequences: A082292 A082293 A082294 * A082296 A082297 A082298

Keyword

nonn

Author

Reinhard Zumkeller, Apr 08 2003

Status

approved