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

1,1

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.

Formula

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

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

Crossrefs

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

Sequence in context: A157322 A172443 A190108 * A145313 A235961 A235572

Adjacent sequences: A308910 A308911 A308912 * A308914 A308915 A308916

Keyword

nonn

Author

Amiram Eldar, Jun 30 2019

Status

approved