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

1,2

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).

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

Example

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.

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

Crossrefs

Cf. A000005, A002182, A067128, A308530.

Sequence in context: A347979 A138286 A355286 * A102290 A025540 A334224

Adjacent sequences: A308529 A308530 A308531 * A308533 A308534 A308535

Keyword

nonn

Author

Amiram Eldar, Jun 06 2019

Status

approved