cp's OEIS Frontend

A369167 a(n) = A000688(n + A000688(n)).

%I A369167 #9 Jan 15 2024 09:50:11
%S A369167 1,1,2,1,1,1,3,1,1,1,2,1,1,1,5,1,2,2,2,1,1,1,3,3,3,3,1,1,1,1,7,1,1,1,
%T A369167 4,3,1,1,3,1,1,1,2,1,1,1,5,1,1,2,2,3,3,1,3,1,1,1,2,1,1,2,1,2,1,1,2,1,
%U A369167 1,1,6,1,1,2,1,1,1,1,5,1,1,1,2,1,1,1,3
%N A369167 a(n) = A000688(n + A000688(n)).
%D A369167 József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter XIII, page 478.
%H A369167 Amiram Eldar, <a href="/A369167/b369167.txt">Table of n, a(n) for n = 1..10000</a>
%H A369167 Haihong Fan and Wenguang Zhai, <a href="https://doi.org/10.3390/sym14091755">A Symmetric Form of the Mean Value Involving Non-Isomorphic Abelian Groups</a>, Symmetry 2022, 14(9), 1755.
%H A369167 Haihong Fan and Wenguang Zhai, <a href="https://doi.org/10.1007/s10986-023-09596-x">On some sums involving the counting function of nonisomorphic Abelian groups</a>, Lithuanian Mathematical Journal, Vol. 63 (2023), pp. 166-180; <a href="https://arxiv.org/abs/2204.02576">arXiv preprint</a>, arXiv:2204.02576 [math.NT], 2022.
%H A369167 Aleksandar Ivić, <a href="https://www.jstor.org/stable/43666434">An asymptotic formula involving the enumerating function of finite abelian groups</a>, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 3 (1992), pp. 61-66.
%F A369167 Sum_{k=1..n} a(k) = c * n + O(n^(k+eps)) for any eps > 0, where c > 0 is a constant and k = 11/12 (Ivić, 1992), 3/4 (Fan and Zhai, 2023), or 2/3 (Fan and Zhai, 2022).
%t A369167 Table[FiniteAbelianGroupCount[n + FiniteAbelianGroupCount[n]], {n, 1, 100}]
%o A369167 (PARI) A000688(n) = vecprod(apply(numbpart, factor(n)[, 2]));
%o A369167 a(n) = A000688(n + A000688(n));
%Y A369167 Cf. A000688, A369162.
%K A369167 nonn,easy
%O A369167 1,3
%A A369167 _Amiram Eldar_, Jan 15 2024