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

1,2

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).

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

Formula

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

Example

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.

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

Crossrefs

Cf. A000005, A002182, A067128, A308530.

Sequence in context: A327998 A274891 A062182 * A073771 A219247 A224094

Adjacent sequences: A308528 A308529 A308530 * A308532 A308533 A308534

Keyword

nonn

Author

Amiram Eldar, Jun 06 2019

Status

approved