A283050 Integers that are divisible by the square of their least prime factor.

4, 8, 9, 12, 16, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 48, 49, 52, 56, 60, 63, 64, 68, 72, 76, 80, 81, 84, 88, 92, 96, 99, 100, 104, 108, 112, 116, 117, 120, 121, 124, 125, 128, 132, 135, 136, 140, 144, 148, 152, 153, 156, 160, 164, 168, 169, 171, 172, 175, 176, 180

Offset: 1

Author

Michel Marcus, Feb 27 2017

Keywords

• nonn

Comments

Integers > 1 such that A126773(n) = 1.

Conjecture: 1 <= a(n+1) - a(n) <= 4. - R. J. Cano, Feb 27 2017

The conjecture is true since all multiples of 4 are in this sequence. - Charles R Greathouse IV, Feb 28 2017

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A013929 (numbers that are not squarefree).

Cf. A126773, A283071.

Programs

Maple

A283050 := proc(n)
    option remember;
    if n =1 then
        4 ;
    else
        for a from procname(n-1)+1 do
            if A126773(a)=  1 then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A283050(n),n=1..100) ; # R. J. Mathar, Mar 03 2017

Mathematica

Select[Range[2, 180], Divisible[#, FactorInteger[#][[1, 1]]^2] &] (* Michael De Vlieger, Feb 27 2017 *)

PARI

isok(n) = !(n % factor(n)[1,1]^2);

Formula

a(n) ~ kn where 1/k = 1/2^2 + 1/2*1/3^2 + 1/2*2/3*1/5^2 + 1/2*2/3*4/5*1/7^2 + ... = A283071 so k = 3.02940306.... - Charles R Greathouse IV, Feb 27 2017