OFFSET
1,2
COMMENTS
Conjecture: a(n) changes sign infinitely often.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
From Seiichi Manyama, Apr 03 2023: (Start)
G.f. A(x) satisfies x = Sum_{k>=1} k^5 * (1 - x^k) * A(x^k).
Sum_{k=1..n} k^5 * a(floor(n/k)) = 1. (End)
MATHEMATICA
Array[Sum[MoebiusMu[k]*k^5, {k, #}] &, 32] (* Michael De Vlieger, Jul 15 2020 *)
PROG
(PARI) a(n) = sum(k=1, n, moebius(k)*k^5); \\ Michel Marcus, Jul 15 2020
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
def A336279(n):
if n <= 1:
return 1
c, j = 1, 2
k1 = n//j
while k1 > 1:
j2 = n//k1 + 1
c -= (j2**2*(j2**2*(j2*(2*j2 - 6) + 5) - 1)-j**2*(j**2*(j*(2*j - 6) + 5) - 1))//12*A336279(k1)
j, k1 = j2, n//j2
return c-(n**2*(n**2*(n*(2*n + 6) + 5) - 1)-j**2*(j**2*(j*(2*j - 6) + 5) - 1))//12 # Chai Wah Wu, Apr 04 2023
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Donald S. McDonald, Jul 15 2020
STATUS
approved