OFFSET
1,3
LINKS
Felix Fröhlich, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = n - Sum_{k=1..n} (1 - ceiling(n/k^2) + floor(n/k^2)).
a(n) = Sum_{k=1..n} sign(n mod k^2). - Wesley Ivan Hurt, May 09 2021
EXAMPLE
a(3) = 2; 1^2|3, but 2^2 and 3^2 do not. So a(3) = 2.
a(4) = 2; 1^2|4 and 2^2|4 but 3^2 and 4^2 do not, So a(4) = 2.
MATHEMATICA
Table[Sum[Ceiling[n/k^2] - Floor[n/k^2], {k, n}], {n, 100}]
PROG
(PARI) a(n) = sum(k=1, n, if (n % k^2, 1)); \\ Michel Marcus, Jan 31 2021
(Python)
from sympy import divisor_count, integer_nthroot
from sympy.ntheory.factor_ import core
def A338228(n):
return n-divisor_count(integer_nthroot(n//core(n, 2), 2)[0]) # Chai Wah Wu, Feb 01 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jan 30 2021
STATUS
approved
