cp's OEIS Frontend

A383055 Numerators of the partial sums of the reciprocals of the number of unitary divisors function (A034444).

%I A383055 #8 Apr 15 2025 10:26:24
%S A383055 1,3,2,5,3,13,15,17,19,5,11,23,25,13,27,29,31,8,17,35,9,37,39,10,21,
%T A383055 43,45,23,12,97,101,105,107,109,111,113,117,119,121,123,127,16,33,67,
%U A383055 17,69,71,18,37,75,19,77,79,20,81,41,83,21,43,173,177,179,181,185
%N A383055 Numerators of the partial sums of the reciprocals of the number of unitary divisors function (A034444).
%D A383055 Jean-Marie De Koninck and Aleksandar Ivić, Topics in Arithmetical Functions, North-Holland Publishing Company, Amsterdam, Netherlands, 1980. See pp. 42-43.
%D A383055 Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, p. 50.
%H A383055 Amiram Eldar, <a href="/A383055/b383055.txt">Table of n, a(n) for n = 1..10000</a>
%H A383055 Jean-Marie De Koninck and Jacques Grah, <a href="http://doi.org/10.4064/cm-79-2-249-272">Arithmetic functions and weighted averages</a>, Colloquium Mathematicum, Vol. 79. No. 2 (1999), pp. 249-272.
%F A383055 a(n) = numerator(Sum_{k=1..n} 1/A034444(k)).
%F A383055 a(n)/A383056(n) = (c/sqrt(Pi)) * n / sqrt(log(n)) + O(n / log(n)^(3/2)), where c = A345288 (De Koninck and Ivić, 1980).
%e A383055 Fractions begin with 1, 3/2, 2, 5/2, 3, 13/4, 15/4, 17/4, 19/4, 5, 11/2, 23/4, ...
%t A383055 Numerator[Accumulate[1/Array[2^PrimeNu[#] &, 100]]]
%o A383055 (PARI) list(nmax) = {my(s = 0); for(k = 1, nmax, s += 1 / 2^omega(k); print1(numerator(s), ", "))};
%Y A383055 The unitary analog of A104528.
%Y A383055 Cf. A002161, A034444, A345288, A383056 (denominators).
%Y A383055 Similar sequences: A064608, A370898, A379513.
%K A383055 nonn,easy,frac
%O A383055 1,2
%A A383055 _Amiram Eldar_, Apr 15 2025