A368673 Number of squarefree numbers less than n that do not divide n.
0, 0, 1, 1, 2, 1, 4, 4, 4, 3, 6, 4, 7, 6, 7, 9, 10, 8, 11, 9, 10, 11, 14, 12, 14, 13, 15, 13, 16, 11, 18, 18, 17, 18, 19, 19, 22, 21, 22, 22, 25, 20, 27, 25, 25, 26, 29, 27, 29, 27, 28, 28, 31, 29, 30, 30, 31, 32, 35, 29, 36, 35, 35, 37, 36, 33, 40, 38, 39, 36, 43
Offset: 1
Examples
a(12) = 4 since there are 4 squarefree numbers less than 12 that do not divide 12, namely: 5, 7, 10, and 11.
Programs
-
Mathematica
Table[Sum[MoebiusMu[k]^2 (Ceiling[n/k] - Floor[n/k]), {k, n}], {n, 100}] -
PARI
a(n) = sum(k=1, n-1, (n % k) && issquarefree(k)); \\ Michel Marcus, Jan 03 2024
-
Python
from math import isqrt from sympy import factorint, mobius def A368673(n): return sum(mobius(k)*((n-1)//k**2) for k in range(1,isqrt(n-1)+1))-(1<