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A255270 Integer part of fourth root of n.

%I A255270 #50 Jun 06 2025 12:15:49
%S A255270 0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%T A255270 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%U A255270 2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3
%N A255270 Integer part of fourth root of n.
%C A255270 n appears (n+1)^4 - n^4 times (A005917).
%H A255270 Bruno Berselli, <a href="/A255270/b255270.txt">Table of n, a(n) for n = 0..1000</a>
%F A255270 a(n) = floor(n^(1/4)) = floor(sqrt(A000196(n))).
%F A255270 G.f.: Sum_{k>=1} x^(k^4)/(1 - x). - _Ilya Gutkovskiy_, Dec 22 2016
%F A255270 a(n) = Sum_{i=1..n} A219009(i)*floor(n/i). - _Ridouane Oudra_, Feb 26 2023
%p A255270 A255270 := proc(n)
%p A255270     floor( n^(1/4)) ;
%p A255270 end proc:
%p A255270 seq(A255270(n),n=0..100) ; # _R. J. Mathar_, May 08 2020
%t A255270 Floor[Range[0, 100]^(1/4)]
%o A255270 (PARI) vector(100, n, n--; floor(n^(1/4)))
%o A255270 (PARI) a(n) = sqrtnint(n, 4); \\ _Michel Marcus_, Dec 22 2016
%o A255270 (Sage) [floor(n^(1/4)) for n in (0..100)]
%o A255270 (Magma) [IsZero(n) select 0 else Iroot(n, 4): n in [0..100]];
%o A255270 (Magma) [Floor(n^(1/4)): n in [0..100]]; // _Vincenzo Librandi_, Feb 20 2015
%o A255270 (Python)
%o A255270 from sympy import integer_nthroot
%o A255270 def A255270(n): return integer_nthroot(n,4)[0] # _Chai Wah Wu_, Jun 06 2025
%Y A255270 Cf. A005917.
%Y A255270 Cf. sequences of the type floor(n^(1/k)): A000196 (k=2), A048766 (k=3), this sequence (k=4), A178487 (k=5), A178489 (k=6).
%Y A255270 Cf. A219009.
%K A255270 nonn,easy
%O A255270 0,17
%A A255270 _Bruno Berselli_, Feb 20 2015