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

7560, 20160, 45360, 50400, 83160, 221760, 498960, 1081080, 2882880, 6486480, 14414400, 17297280, 32432400, 43243200, 110270160, 245044800, 294053760, 551350800, 2095133040, 2205403200, 4655851200, 5587021440, 10475665200, 64250746560, 73329656400, 97772875200

Offset: 1

Author

Amiram Eldar, Jun 30 2019

Keywords

• nonn

Comments

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.

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).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• S. Sivasankaranarayana Pillai, On numbers analogous to highly composite numbers of Ramanujan, Rajah Sir Annamalai Chettiar Commemoration Volume, ed. Dr. B. V. Narayanaswamy Naidu, Annamalai University, 1941, pp. 697-704.
• S. Sivasankaranarayana Pillai, Highly Composite Numbers of the t th Order, J. Indian Math. Soc., Vol. 8 (1944), pp. 61-74.

Crossrefs

Cf. A002182, A004394, A166735, A166981, A181309.

Programs

Mathematica

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

Formula

a(2118+i) = A002182(2567+i) for i > 0.