This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A379359 #8 Dec 22 2024 16:52:28
%S A379359 1,2,3,7,9,11,13,41,22,25,28,59,65,71,77,391,421,218,233,481,511,541,
%T A379359 571,581,298,313,106,217,227,237,247,1739,1809,1879,1949,3933,4073,
%U A379359 4213,4353,13199,13619,14039,14459,14669,14879,15299,15719,15803,16013,16223,16643
%N A379359 Numerators of the partial sums of the reciprocals of the number of abelian groups function (A000688).
%D A379359 Jean-Marie De Koninck and Aleksandar Ivić, Topics in Arithmetical Functions, North-Holland Publishing Company, Amsterdam, Netherlands, 1980. See pp. 13-16, Theorem 1.3.
%D A379359 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003. See section 5.1, Abelian group enumeration constants, p. 274.
%H A379359 Amiram Eldar, <a href="/A379359/b379359.txt">Table of n, a(n) for n = 1..10000</a>
%H A379359 László Tóth, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Toth/toth25.html">Alternating Sums Concerning Multiplicative Arithmetic Functions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. See section 4.8, pp. 27-28.
%F A379359 a(n) = numerator(Sum_{k=1..n} 1/A000688(k)).
%F A379359 a(n)/A379360(n) = D * n + O(sqrt(n/log(n))), where D = A084911.
%e A379359 Fractions begin with 1, 2, 3, 7/2, 9/2, 11/2, 13/2, 41/6, 22/3, 25/3, 28/3, 59/6, ...
%t A379359 Numerator[Accumulate[Table[1/FiniteAbelianGroupCount[n], {n, 1, 100}]]]
%o A379359 (PARI) f(n) = vecprod(apply(numbpart, factor(n)[, 2]));
%o A379359 list(nmax) = {my(s = 0); for(k = 1, nmax, s += 1 / f(k); print1(numerator(s), ", "))};
%Y A379359 Cf. A000688, A063966, A084911, A370897, A379360 (denominators), A379361.
%K A379359 nonn,easy,frac
%O A379359 1,2
%A A379359 _Amiram Eldar_, Dec 21 2024