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

1,2

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.

Links

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

Formula

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

Example

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).

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

Crossrefs

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

Sequence in context: A019550 A117304 A022759 * A091193 A335541 A174018

Adjacent sequences: A335537 A335538 A335539 * A335541 A335542 A335543

Keyword

nonn

Author

Amiram Eldar, Jun 13 2020

Status

approved