A335540 Numbers with a record number of abundant divisors.

1, 12, 24, 36, 60, 72, 120, 180, 240, 360, 720, 1080, 1440, 1680, 2160, 2520, 3360, 4320, 5040, 7560, 10080, 15120, 20160, 25200, 30240, 40320, 45360, 50400, 55440, 60480, 75600, 90720, 100800, 110880, 151200, 166320, 221760, 277200, 302400, 332640, 443520, 554400

Offset: 1

Author

Amiram Eldar, Jun 13 2020

Keywords

• nonn

Comments

The corresponding numbers of abundant divisors are 0, 1, 2, 3, 4, 5, 7, 8, 10, 13, 18, 19, 23, ...

All the terms > 1 are abundant numbers (A005101) and all the terms > 12 are not primitive abundant numbers (A091191).

Apparently, all the terms are least numbers of their prime signature (A025487). This was verified for the first 100 terms.

Examples

			12 is in the sequence since it is the least number with one abundant divisor (12). The next number with more than one abundant divisor is 24 which has 2 abundant divisors (12 and 24).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000203, A005101, A025487, A080224, A091191, A091193, A335541, A335542.

Programs

Mathematica

s[n_] := Count[Divisors[n], _?(DivisorSigma[1, #] > 2*# &)]; sm = -1; seq = {}; Do[s1 = s[n]; If[s1 > sm, sm = s1; AppendTo[seq, n]], {n, 1, 10^6}]; seq

Formula

Numbers m such that A080224(m) > A080224(k) for all k < m.