A082294 Numbers having exactly two square divisors > 1.

16, 32, 48, 80, 81, 96, 112, 160, 162, 176, 208, 224, 240, 243, 272, 304, 336, 352, 368, 405, 416, 464, 480, 486, 496, 528, 544, 560, 567, 592, 608, 624, 625, 656, 672, 688, 736, 752, 810, 816, 848, 880, 891, 912, 928, 944, 976, 992, 1040, 1053, 1056, 1072

Offset: 1

Author

Reinhard Zumkeller, Apr 08 2003

Keywords

• nonn

Comments

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

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

Examples

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

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A082295, A046951, A048111, A013929.

Programs

Mathematica

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

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

Formula

A046951(a(n)) = 3.