A230501 Floor(Sum(d(k), k=1..n)/n), where d(k) is the number of divisors of k.

1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset

1,4

Comments

Except for n=0, a(n) = floor(A006218(n)/n).

Links

Table of n, a(n) for n=1..87.

Wikipedia, Divisor Summatory Function

Mathematica

Table[Floor[Sum[DivisorSigma[0, k], {k, n}]/n], {n, 100}] (* T. D. Noe, Oct 22 2013 *)

Prog

(Python)
from math import isqrt
def A230501(n): return (-(s:=isqrt(n))**2+(sum(n//k for k in range(1, s+1))<<1))//n # Chai Wah Wu, Oct 23 2023

Crossrefs

Cf. A000005, A006218.

Sequence in context: A076925 A100961 A263206 * A287272 A300287 A226764

Adjacent sequences: A230498 A230499 A230500 * A230502 A230503 A230504

Keyword

nonn

Author

Jon Perry, Oct 21 2013

Status

approved