OFFSET
0,2
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = 2*n*(4*n^2 + 6*n + 3) - Sum_{j=2..n} a(floor(n/j)). - Chai Wah Wu, Mar 30 2021
MATHEMATICA
Table[If[n>0, 8 * Sum[MoebiusMu[k] * ((Floor[n/k] + 1)^3 - 1), {k, 1, n}] - 24 * Sum[EulerPhi[k], {k, 1, n}] - 6, 0], {n, 0, 35}] (* Indranil Ghosh, Mar 11 2017 *)
PROG
(PARI) a(n)=if(n>0, 8*sum(k=1, n, moebius(k)*((n\k+1)^3-1))-24*sum(k=1, n, eulerphi(k))-6)
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
def A175549(n):
if n == 0:
return 0
c, j = 0, 2
k1 = n//j
while k1 > 1:
j2 = n//k1 + 1
c += (j2-j)*A175549(k1)
j, k1 = j2, n//j2
return 4*n*(n - 1)*(2*n + 5)-c+26*(j-1)# Chai Wah Wu, Mar 30 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Charles R Greathouse IV, Jun 24 2010
EXTENSIONS
Edited by Charles R Greathouse IV, Jul 19 2010
STATUS
approved