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A209802
Partial sums of exponential Möbius function, A166234.
4
1, 2, 3, 2, 3, 4, 5, 4, 3, 4, 5, 4, 5, 6, 7, 7, 8, 7, 8, 7, 8, 9, 10, 9, 8, 9, 8, 7, 8, 9, 10, 9, 10, 11, 12, 13, 14, 15, 16, 15, 16, 17, 18, 17, 16, 17, 18, 18, 17, 16, 17, 16, 17, 16, 17, 16, 17, 18, 19, 18, 19, 20, 19, 20, 21, 22, 23, 22, 23, 24, 25, 26
OFFSET
1,2
COMMENTS
Analog of Mertens's function, A002321; conjecture: a(n) > 0.
Values of a(10^n) at n = 1, 2, 3, ...: 4, 34, 355, 3610, 36116, 360967, 3609566, 36094237, .... - Charles R Greathouse IV, Sep 02 2015
LINKS
László Tóth, On certain arithmetic functions involving exponential divisors, II, Annales Univ. Sci. Budapest., Sect. Comp., Vol. 27 (2007), pp. 155-166; arXiv preprint, arXiv:0708.3557 [math.NT], 2007-2009.
FORMULA
a(n) ~ c * n, where c = Product_{p prime} (1 + Sum_{k>=2} (mu(k) - mu(k-1))/p^k) = 0.3609447238... (Tóth, 2007). - Amiram Eldar, Nov 08 2020
MATHEMATICA
f[p_, e_] := MoebiusMu[e]; em[n_] := Times @@ f @@@ FactorInteger[n]; Accumulate @ Array[em, 100] (* Amiram Eldar, Nov 08 2020 *)
PROG
(Haskell)
a209802 n = a209802_list !! (n-1)
a209802_list = scanl1 (+) a166234_list
(PARI) first(n)=my(s); vector(n, k, s+=factorback(apply(moebius, factor(k)[, 2]))) \\ Charles R Greathouse IV, Sep 02 2015
(PARI) a(n)=sum(k=1, n, factorback(apply(moebius, factor(k)[, 2]))) \\ Charles R Greathouse IV, Sep 02 2015
CROSSREFS
Sequence in context: A125929 A309236 A071933 * A064672 A138554 A063772
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Mar 13 2012
STATUS
approved