|
| |
|
|
A070889
|
|
Denominator of Sum_{k=1..n} mu(k)/k.
|
|
5
|
|
|
|
1, 2, 6, 6, 30, 15, 105, 105, 105, 210, 2310, 2310, 30030, 15015, 5005, 5005, 85085, 85085, 1616615, 1616615, 4849845, 9699690, 223092870, 223092870, 223092870, 111546435, 111546435, 111546435, 3234846615, 2156564410, 66853496710
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
a(6) = 15 because 1 - 1/2 - 1/3 - 1/5 + 1/6 = 4/30 = 2/15.
|
|
|
MATHEMATICA
|
Table[ Denominator[ Sum[ MoebiusMu[k]/k, {k, 1, n}]], {n, 1, 37}]
|
|
|
PROG
|
(PARI) t = 0; v = []; for( n = 1, 30, t = t + moebius( n) / n; v = concat( v, denominator( t))); v
(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,nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
