OFFSET
1,2
REFERENCES
I. M. Vinogradov, Elements of the Theory of Numbers,(in Russian), Moscow, 1981, p. 36.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..500 from Harry J. Smith)
FORMULA
a(n) = Sum_{d>=1} mu(d)*floor(n/d^3), mu(d) = Moebius function A008683.
a(n) is asymptotic to (1/zeta(3))*n, see A088453. - Benoit Cloitre, Jun 13 2007
a(n) = Sum_{k = 1..n} A212793(k). - Reinhard Zumkeller, May 27 2012
PROG
(PARI) a(n)=sum(k=1, n, moebius(k)*floor(n/k^3)) \\ Benoit Cloitre, Jun 13 2007
(PARI) for (n=1, 500, a=sum(k=1, n, moebius(k)*floor(n/k^3)); write("b060431.txt", n, " ", a)) \\ Harry J. Smith, Jul 05 2009
(PARI) a(n)=my(s); forsquarefree(k=1, sqrtnint(n, 3), s+=n\k[1]^3*moebius(k)); s \\ Charles R Greathouse IV, Jan 08 2018
(Haskell)
a060431 n = a060431_list !! (n-1)
a060431_list = scanl1 (+) a212793_list -- Reinhard Zumkeller, May 27 2012
(Magma) [&+[MoebiusMu(d)*Floor(n div d^3):d in [1..n]]:n in [1..75]]; // Marius A. Burtea, Oct 02 2019
(Python)
from sympy import mobius, integer_nthroot
def A060431(n): return sum(mobius(k)*(n//k**3) for k in range(1, integer_nthroot(n, 3)[0]+1)) # Chai Wah Wu, Aug 06 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Apr 06 2001
STATUS
approved