A344624 a(n) = Sum_{k=1..n} k^c(k), where c(n) is the characteristic function of squares.

1, 2, 3, 7, 8, 9, 10, 11, 20, 21, 22, 23, 24, 25, 26, 42, 43, 44, 45, 46, 47, 48, 49, 50, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 260

Offset

1,2

Comments

For 1 <= k <= n, take a running total: add k if k is a perfect square, otherwise add 1. For example, a(12) = 1+1+1+4+1+1+1+1+9+1+1+1 = 23.

Links

Table of n, a(n) for n=1..64.

Formula

a(n) = n+m*(m-1)*(2*m+5)/6 where m = floor(sqrt(n)). - Chai Wah Wu, May 24 2021

Mathematica

Table[Sum[i^(Floor[Sqrt[i]] - Floor[Sqrt[i - 1]]), {i, n}], {n, 80}]

Prog

(Python 3.8+)
from math import isqrt
def A344624(n):
    m = isqrt(n)
    return n + m*(m-1)*(2*m+5)//6 # Chai Wah Wu, May 24 2021

Crossrefs

Cf. A010052.

Sequence in context: A326979 A326874 A118374 * A154432 A251391 A047361

Adjacent sequences: A344621 A344622 A344623 * A344625 A344626 A344627

Keyword

nonn

Author

Wesley Ivan Hurt, May 24 2021

Status

approved