A308531 Largely composite numbers (A067128) with a unique number of divisors.

1, 4, 36, 48, 180, 720, 5040, 20160, 25200, 45360, 50400, 498960, 665280, 3603600, 6486480, 7207200, 8648640, 14414400, 32432400, 110270160, 698377680, 2095133040, 2205403200, 41902660800, 73329656400, 146659312800, 240940299600, 293318625600, 963761198400

Offset: 1

Author

Amiram Eldar, Jun 06 2019

Keywords

• nonn

Comments

These are highly composite numbers (A002182) that have no other largely composite numbers with the same number of divisors.

The corresponding numbers of divisors d(a(n)) are 1, 3, 9, 10, 18, 30, 60, 84, 90, 100, ... (see the link for more values).

Examples

			4 is in the sequence since it is the only largely composite number with 3 divisors.
2 is not in the sequence since it has 2 divisors, the same as the next largely composite number 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..114
• Amiram Eldar, Table of n, a(n), d(a(n)) for n = 1..114

Crossrefs

Cf. A000005, A002182, A067128, A308530.

Programs

Mathematica

s = {}; dm = 1; c = 0; nprev = 1; Do[d = DivisorSigma[0, n]; If[d == dm, c++]; If[d > dm, dm = d; If[c == 1, AppendTo[s, nprev]]; c = 1; nprev = n], {n, 1, 10^8}]; s

Formula

A002182(k) is in the sequence if A308530(k) = 1.