A339363 a(n) = Sum_{k=1..floor(sqrt(n))} floor(sqrt(n-k)).

0, 1, 1, 2, 3, 4, 4, 4, 6, 7, 8, 9, 9, 9, 9, 12, 13, 14, 15, 16, 16, 16, 16, 16, 20, 21, 22, 23, 24, 25, 25, 25, 25, 25, 25, 30, 31, 32, 33, 34, 35, 36, 36, 36, 36, 36, 36, 36, 42, 43, 44, 45, 46, 47, 48, 49, 49, 49, 49, 49, 49, 49, 49, 56, 57, 58, 59, 60, 61, 62, 63, 64, 64, 64

Offset: 1

Author

Wesley Ivan Hurt, Apr 24 2021

Keywords

• nonn

Comments

Contains all nonnegative integers not in A189151.

Crossrefs

Cf. A189151.

Programs

Mathematica

Table[Sum[Floor[Sqrt[n - k]], {k, Floor[Sqrt[n]]}], {n, 80}]

PARI

a(n) = sum(k=1, sqrtint(n), sqrtint(n-k)); \\ Michel Marcus, Apr 24 2021

Python

from math import isqrt
def a(n): return sum(isqrt(n-k) for k in range(1, isqrt(n)+1))
print([a(n) for n in range(1, 75)]) # Michael S. Branicky, Apr 24 2021