cp's OEIS Frontend

A308913 Highly composite numbers (A002182) that are not superabundant numbers (A004394).

%I A308913 #14 Jul 01 2019 03:57:01
%S A308913 7560,20160,45360,50400,83160,221760,498960,1081080,2882880,6486480,
%T A308913 14414400,17297280,32432400,43243200,110270160,245044800,294053760,
%U A308913 551350800,2095133040,2205403200,4655851200,5587021440,10475665200,64250746560,73329656400,97772875200
%N A308913 Highly composite numbers (A002182) that are not superabundant numbers (A004394).
%C A308913 Pillai noted in 1941 that 7560 is the first term of this sequence. He also asked for the opposite sequence and wondered whether its first term (A166735(1) = 1163962800) is within the reach of modern computation.
%C A308913 Since the sequence of superabundant numbers that are also highly composite, A166981, is finite, this sequence contains all the highly composite numbers above A002182(2567) = A004394(1023).
%H A308913 Amiram Eldar, <a href="/A308913/b308913.txt">Table of n, a(n) for n = 1..10000</a>
%H A308913 S. Sivasankaranarayana Pillai, <a href="https://archive.org/details/in.ernet.dli.2015.282686/page/n825">On numbers analogous to highly composite numbers of Ramanujan</a>, Rajah Sir Annamalai Chettiar Commemoration Volume, ed. Dr. B. V. Narayanaswamy Naidu, Annamalai University, 1941, pp. 697-704.
%H A308913 S. Sivasankaranarayana Pillai, <a href="http://www.informaticsjournals.com/index.php/jims/article/view/17091">Highly Composite Numbers of the t th Order</a>, J. Indian Math. Soc., Vol. 8 (1944), pp. 61-74.
%F A308913 a(2118+i) = A002182(2567+i) for i > 0.
%t A308913 seq = {}; dm = 0; sm = 0; Do[d = DivisorSigma[0, n]; s = DivisorSigma[1, n]; If[d > dm, dm = d]; If[s > s, sm = s, AppendTo[seq, n]], {n, 1, 3000000}]; seq
%Y A308913 Cf. A002182, A004394, A166735, A166981, A181309.
%K A308913 nonn
%O A308913 1,1
%A A308913 _Amiram Eldar_, Jun 30 2019