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

1,2

Links

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

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A079645, A228318.

Sequence in context: A080197 A341749 A115847 * A032966 A122937 A246076

Adjacent sequences: A204312 A204313 A204314 * A204316 A204317 A204318

Keyword

nonn

Author

Benoit Cloitre, Jan 14 2012

Status

approved