A308532 Highly composite numbers (A002182) with a record number of largely composite numbers (A067128) having the same number of divisors.

1, 2, 6, 60, 360, 73513440, 1396755360, 4497552259200, 130429015516800, 149602080797769600, 4488062423933088000, 6133685312708553600, 184010559381256608000, 7912454053394034144000, 19709923047004539052704000, 1162885459773267804109536000, 780296143507862696557498656000

Offset: 1

Author

Amiram Eldar, Jun 06 2019

Keywords

• nonn

Comments

The corresponding record numbers of divisors d(a(n)) are 1, 2, 3, 6, 9, 10, 11, 14, 16, 20, ... (see the link for more values).

Examples

			6 is in the sequence since there are a record number of 3 largely composite numbers, 6, 8, and 10 with the same number of divisors. The next record is of 60, with 6 largely composite numbers, 60, 72, 84, 90, 96, and 108, with the same number of divisors.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..25
• Amiram Eldar, Table of n, a(n), d(a(n)) for n = 1..25

Crossrefs

Cf. A000005, A002182, A067128, A308530.

Programs

Mathematica

s = {}; dm = 1; c = 0; cm = 0; nprev = 1; Do[d = DivisorSigma[0, n]; If[d == dm, c++]; If[d > dm, dm = d; If[c > cm, cm = c; AppendTo[s, nprev]]; c = 1; nprev = n], {n, 1, 10^3}]; s