login
Numbers having exactly two square divisors > 1.
5

%I #25 Sep 25 2022 04:26:24

%S 16,32,48,80,81,96,112,160,162,176,208,224,240,243,272,304,336,352,

%T 368,405,416,464,480,486,496,528,544,560,567,592,608,624,625,656,672,

%U 688,736,752,810,816,848,880,891,912,928,944,976,992,1040,1053,1056,1072

%N Numbers having exactly two square divisors > 1.

%C Numbers of the form p^e * s where p is prime, e is 4 or 5 and s is squarefree and coprime to p. - _David A. Corneth_, Sep 01 2020

%C The asymptotic density of this sequence is (6/Pi^2) * Sum_{p prime} (1/(p^3*(p+1)) + 1/(p^4*(p+1))) = 0.04680621631952059947... . - _Amiram Eldar_, Sep 25 2022

%H David A. Corneth, <a href="/A082294/b082294.txt">Table of n, a(n) for n = 1..10000</a>

%F A046951(a(n)) = 3.

%e 81 has 3 square divisors: 1, 9 and 81, therefore 81 is a term.

%t Select[Range[1000], MemberQ[{{4}, {5}}, Select[FactorInteger[#][[;;,2]], #1 > 1 &]] &] (* _Amiram Eldar_, Sep 01 2020 *)

%o (PARI) is(n)=my(f=vecsort(factor(n)[,2],,4)); if(#f==1, f[1]>3&&f[1]<6, #f>1 && f[1]>3 && f[1]<6 && f[2]==1) \\ _Charles R Greathouse IV_, Oct 16 2015

%Y Cf. A082295, A046951, A048111, A013929.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Apr 08 2003