cp's OEIS Frontend

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

%I A204315 #35 Oct 08 2023 09:03:53
%S A204315 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,
%T A204315 38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,81,
%U A204315 84,87,90,93,96,99,102,105,108,111,114,117,120,123,126
%N A204315 Numbers j such that floor(j^(1/4)) divides j.
%H A204315 David A. Corneth, <a href="/A204315/b204315.txt">Table of n, a(n) for n = 1..11115</a>
%F A204315 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
%e A204315 26 is a term as floor(26^(1/4)) = 2 divides 26. - _David A. Corneth_, Oct 04 2023
%p A204315 isA204315 := proc(n)
%p A204315     if modp(n,floor(root[4](n))) = 0 then
%p A204315         true ;
%p A204315     else
%p A204315         false ;
%p A204315     fi ;
%p A204315 end proc:
%p A204315 for n from 1 to 130 do
%p A204315     if isA204315(n) then
%p A204315         printf("%d,",n) ;
%p A204315     end if;
%p A204315 end do: # _R. J. Mathar_, Sep 10 2017
%t A204315 Select[Range[150],Mod[#,Floor[Surd[#,4]]]==0&] (* _Harvey P. Dale_, Oct 04 2023 *)
%o A204315 (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
%o A204315 (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
%Y A204315 Cf. A079645, A228318.
%K A204315 nonn
%O A204315 1,2
%A A204315 _Benoit Cloitre_, Jan 14 2012