A204315 Numbers j such that floor(j^(1/4)) divides j.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126

Offset: 1

Author

Benoit Cloitre, Jan 14 2012

Keywords

• nonn

Examples

			26 is a term as floor(26^(1/4)) = 2 divides 26. - _David A. Corneth_, Oct 04 2023
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..11115

Crossrefs

Cf. A079645, A228318.

Programs

Maple

isA204315 := proc(n)
    if modp(n,floor(root[4](n))) = 0 then
        true ;
    else
        false ;
    fi ;
end proc:
for n from 1 to 130 do
    if isA204315(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Sep 10 2017

Mathematica

Select[Range[150],Mod[#,Floor[Surd[#,4]]]==0&] (* Harvey P. Dale, Oct 04 2023 *)

PARI

a(n) = {my(k = 0, t = 0); while(t < n, k++; t = 4*k^3/3 + 5*k^2 + 26*k/3); (k+1)^4 - 1 - k * (t - n)} \\ David A. Corneth, Oct 06 2023

PARI

first(n) = {my(res = vector(n), t = 0); for(i = 1, oo, forstep(j = i^4, (i + 1)^4 - 1, i, t++; if(t > n, return(res)); res[t] = j))} \\ David A. Corneth, Oct 06 2023

Formula

Let f(x) = 4*x^3/3 + 5*x^2 + 26*x/3 and let k be the smallest integer x such that f(x) >= n. Then a(n) = (k+1)^4 - 1 - k * (f(k) - n). - David A. Corneth, Oct 06 2023