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A070889

Denominator of Sum_{k=1..n} mu(k)/k.

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

Amiram Eldar, Table of n, a(n) for n = 1..2370

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)

def A070889(n): return f(n).denominator # Chai Wah Wu, Nov 03 2023

CROSSREFS

Cf. A008683, A068337, A070888 (numerators).

Sequence in context: A333196 A216850 A379582 * A072744 A374317 A056042

Adjacent sequences: A070886 A070887 A070888 * A070890 A070891 A070892

KEYWORD

frac,nonn

AUTHOR

Donald S. McDonald, May 17 2002

EXTENSIONS

Edited by Robert G. Wilson v, Jun 10 2002

STATUS

approved

URL: https://oeis.org/A070889

⇱ A070889 - OEIS