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Superabundant numbers (A004394) that are not highly composite (A002182).
7

%I #21 Dec 18 2019 02:44:41

%S 1163962800,4658179125600,13974537376800,144403552893600,

%T 433210658680800,10685862914126400,21371725828252800,

%U 32057588742379200,37400520199442400,64115177484758400,1533421328177138400

%N Superabundant numbers (A004394) that are not highly composite (A002182).

%C Alaoglu and Erdos mention the first term in footnote 14.

%C Because the "shapes" of superabundant and highly composite numbers are different, there is a last superabundant number that is also highly composite. In factored form, that 154-digit number is N = A004394(1023) = A002182(2567) = 2^10 3^6 5^4 7^3 11^3 13^2 17^2 19^2 23^2 29 31 37...347. In other words, this sequence contains all superabundant numbers greater than N. - _T. D. Noe_, Oct 26 2009

%H T. D. Noe, <a href="/A166735/b166735.txt">Table of n, a(n) for n = 1..574</a>

%H L. Alaoglu and P. Erdos, <a href="http://www.renyi.hu/~p_erdos/1944-03.pdf">On highly composite and similar numbers,</a> Trans. Amer. Math. Soc., 56 (1944), 448-469. <a href="http://upforthecount.com/math/errata.html">Errata</a>

%H Thomas Fink, <a href="https://arxiv.org/abs/1912.07979">Recursively divisible numbers</a>, arXiv:1912.07979 [math.NT], 2019. Mentions this sequence.

%H S. Ramanujan, <a href="http://ramanujan.sirinudi.org/Volumes/published/ram15.html">Highly composite numbers</a>, Proceedings of the London Mathematical Society, 2, XIV, 1915, 347 - 409.

%H S. Ramanujan, <a href="http://dx.doi.org/10.1023/A:1009764017495">Highly composite numbers</a>, Annotated and with a foreword by J.-L. Nicolas and G. Robin, Ramanujan J., 1 (1997), 119-153.

%F a(574+i) = A004394(1023+i) for i>0.

%Y Cf. A166981 (intersection of SA and HC numbers). - _T. D. Noe_, Oct 26 2009

%Y Cf. A189228 (SA numbers that are not CA).

%K nonn

%O 1,1

%A _T. D. Noe_, Oct 20 2009