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A070889 Denominator of Sum_{k=1..n} mu(k)/k.

%I A070889 #21 Nov 03 2023 17:01:58
%S A070889 1,2,6,6,30,15,105,105,105,210,2310,2310,30030,15015,5005,5005,85085,
%T A070889 85085,1616615,1616615,4849845,9699690,223092870,223092870,223092870,
%U A070889 111546435,111546435,111546435,3234846615,2156564410,66853496710
%N A070889 Denominator of Sum_{k=1..n} mu(k)/k.
%H A070889 Amiram Eldar, <a href="/A070889/b070889.txt">Table of n, a(n) for n = 1..2370</a>
%e A070889 a(6) = 15 because 1 - 1/2 - 1/3 - 1/5 + 1/6 = 4/30 = 2/15.
%t A070889 Table[ Denominator[ Sum[ MoebiusMu[k]/k, {k, 1, n}]], {n, 1, 37}]
%o A070889 (PARI) t = 0; v = []; for( n = 1, 30, t = t + moebius( n) / n; v = concat( v, denominator( t))); v
%o A070889 (Python)
%o A070889 from functools import lru_cache
%o A070889 from sympy import harmonic
%o A070889 @lru_cache(maxsize=None)
%o A070889 def f(n):
%o A070889     if n <= 1:
%o A070889         return 1
%o A070889     c, j = 1, 2
%o A070889     k1 = n//j
%o A070889     while k1 > 1:
%o A070889         j2 = n//k1 + 1
%o A070889         c += (harmonic(j-1)-harmonic(j2-1))*f(k1)
%o A070889         j, k1 = j2, n//j2
%o A070889     return c+harmonic(j-1)-harmonic(n)
%o A070889 def A070889(n): return f(n).denominator # _Chai Wah Wu_, Nov 03 2023
%Y A070889 Cf. A008683, A068337, A070888 (numerators).
%K A070889 frac,nonn
%O A070889 1,2
%A A070889 _Donald S. McDonald_, May 17 2002
%E A070889 Edited by _Robert G. Wilson v_, Jun 10 2002