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%I #7 Jan 15 2024 09:44:07
%S 1,16,32,64,81,128,243,256,512,576,625,729,768,1024,1152,1280,1296,
%T 1536,1600,1728,1792,2048,2187,2304,2401,2560,2592,2816,2916,3072,
%U 3125,3136,3200,3328,3456,3584,3888,4096,4352,4608,4864,5120,5184,5632,5832,5888,6144
%N Numbers k such that A000005(k) <= A000688(k).
%C The asymptotic density of this sequence is 0 (Ivić, 1983).
%D József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter II, page 73.
%H Amiram Eldar, <a href="/A369170/b369170.txt">Table of n, a(n) for n = 1..10000</a>
%H Aleksandar Ivić, <a href="https://doi.org/10.1016/0022-314X(83)90037-9">On the number of abelian groups of a given order and on certain related multiplicative functions</a>, Journal of Number Theory, Vol. 16, No. 1 (1983), pp. 119-137.
%F The number of terms not exceeding x, N(x) << x / log(x)^(1-eps) for every 0 < eps < 1 (Ivić, 1983).
%t Select[Range[6000], DivisorSigma[0, #] <= FiniteAbelianGroupCount[#] &]
%o (PARI) is(n) = {my(e = factor(n)[,2]); vecprod(apply(x -> x+1, e)) <= vecprod(apply(numbpart, e));}
%Y Cf. A000005, A000688.
%Y Subsequences: A369168, A369169.
%K nonn,easy
%O 1,2
%A _Amiram Eldar_, Jan 15 2024