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A335540
Numbers with a record number of abundant divisors.
4
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jun 13 2020
STATUS
approved