OFFSET
1,3
COMMENTS
Probably the partial sums of A102309. - Ralf Stephan, Jan 03 2005
LINKS
R. J. Mathar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = (A071778(n)-1)/6. - Vladeta Jovovic, Nov 30 2004
a(n) = (1/6)*(-1 + Sum_{k=1..n} moebius(k)*floor(n/k)^3). - Ralf Stephan, Jan 03 2005
MAPLE
f:=proc(n) local i, j, k, t1, t2, t3; t1:=0; for i from 1 to n do for j from i to n do t2:=gcd(i, j); for k from j+1 to n do t3:=gcd(t2, k); if t3 = 1 then t1:=t1+1; fi; od: od: od: t1; end;
MATHEMATICA
f[n_] := Length[ Union[ Flatten[ Table[ If[ GCD[i, j, k] == 1, {i, j, k}], {i, n}, {j, i, n}, {k, j + 1, n}], 2]]]; Table[ If[n > 3, f[n] - 1, f[n]], {n, 47}] (* Robert G. Wilson v, Dec 14 2004 *)
PROG
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
def A100448(n):
if n == 0:
return 0
c, j = 2, 2
k1 = n//j
while k1 > 1:
j2 = n//k1 + 1
c += (j2-j)*(6*A100448(k1)+1)
j, k1 = j2, n//j2
return (n*(n**2-1)-c+j)//6 # Chai Wah Wu, Mar 29 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 21 2004
EXTENSIONS
More terms from Robert G. Wilson v, Dec 14 2004
Edited by N. J. A. Sloane, Sep 06 2008 at the suggestion of R. J. Mathar
STATUS
approved