A349993 - OEIS

%I #28 Mar 20 2022 06:36:16

%S 1,1,1,3,5,7,9,12,15,19,22,26,30,34,39,44,49,54,59,64,70,76,82,88,94,

%T 101,107,114,121,128,135,142,150,157,165,173,181,189,197,205,213,222,

%U 231,239,248,257,266,276,285,295,304,314,323,333,343,353,364,374,384,395,405

%N a(n) is the number of squares k^2 with n^2 <= k^2 <= n^3.

%C Interval with n^2 and n^3 excluded is A349662.

%H Karl-Heinz Hofmann, <a href="/A349993/b349993.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = floor(sqrt(n^3)) - n + 1. - _Giorgos Kalogeropoulos_, Dec 08 2021

%t Table[Floor[Sqrt[n^3]]-n+1,{n,0,100}] (* _Giorgos Kalogeropoulos_, Dec 08 2021 *)

%o (PARI) a(n) = sqrtint(n^3) - n + 1

%o (PARI) a(n)=sum(k=n^2,n^3,issquare(k))

%o (PARI) for(n=0,60,my(n2=n^2,n3=n^3);print1(sum(k=n2,n3,issquare(k)),", "))

%o (Python)

%o def a(n):

%o     counter = 0

%o     while (n+counter)**2 <= n**3: counter += 1

%o     return (counter)

%o print([a(n) for n in range(0,60)])

%o (Python)

%o from math import isqrt

%o def A349993(n): return isqrt(n**3) - n + 1 # _Chai Wah Wu_, Dec 08 2021

%Y Cf. A000290, A000578.

%Y Cf. A349662 (number of squares k^2 with n^2 < k^2 < n^3).

%Y Cf. A028387 (Also the number of squares between (n+2)^2 and (n+2)^4).

%K nonn,easy

%O 0,4

%A _Karl-Heinz Hofmann_ and _Hugo Pfoertner_, Dec 08 2021