|
|
A070888
|
|
Numerator of Sum_{k=1..n} mu(k)/k.
|
|
6
|
|
|
1, 1, 1, 1, -1, 2, -1, -1, -1, 19, -1, -1, -2323, -89, 304, 304, 163, 163, -81988, -81988, -15019, 410857, -249979, -249979, -249979, 4165258, 4165258, 4165258, 9246047, -65721449, -4193929329, -4193929329, -6504197377, -302679716, 2562470143
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,6
|
|
COMMENTS
|
|
|
REFERENCES
|
Harold M. Edwards, Riemann's Zeta Function, Dover Publications, New York, 1974 (ISBN 978-0-486-41740-0), p. 92.
Edmund Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Chelsea Publishing, NY 1953, p. 568.
|
|
LINKS
|
|
|
EXAMPLE
|
a(6) = 2 because 1-1/2-1/3-1/5+1/6 = 4/30 = 2/15.
|
|
MAPLE
|
T:= 0:
for n from 1 to 100 do
T:= T + numtheory:-mobius(n)/n;
A[n]:= numer(T)
od:
|
|
MATHEMATICA
|
Table[ Numerator[ Sum[ MoebiusMu[k]/k, {k, 1, n}]], {n, 1, 37}]
|
|
PROG
|
(PARI) t = 0; v = []; for( n = 1, 60, t= t + moebius( n) / n; v = concat( v, numerator( t))); v \\ adapted to latest PARI version by Michel Marcus, Aug 04 2014
(Python)
from functools import lru_cache
from sympy import harmonic
@lru_cache(maxsize=None)
def f(n):
if n <= 1:
return 1
c, j = 1, 2
k1 = n//j
while k1 > 1:
j2 = n//k1 + 1
c += (harmonic(j-1)-harmonic(j2-1))*f(k1)
j, k1 = j2, n//j2
return c+harmonic(j-1)-harmonic(n)
|
|
CROSSREFS
|
|
|
KEYWORD
|
frac,sign
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|