A309141 Nonunitary highly composite numbers: numbers with a record number of nonunitary divisors.

1, 4, 8, 16, 24, 36, 48, 72, 144, 216, 288, 360, 576, 720, 1080, 1440, 2160, 2880, 3600, 4320, 5040, 7200, 7560, 10080, 15120, 20160, 25200, 30240, 45360, 50400, 60480, 75600, 100800, 110880, 151200, 221760, 277200, 302400, 332640, 453600, 498960, 554400, 665280

Offset: 1

Author

Amiram Eldar, Jul 14 2019

Keywords

• nonn

Comments

Numbers k with A048105(k) > A048105(j) for all j < k.

The corresponding values of records are 0, 1, 2, 3, 4, 5, 6, 8, 11, 12, 14, 16, 17, 22, 24, 28, 32, 34, 37, 40, 44, 46, 48, 56, 64, 68, 74, 80, 84, 92, 96, ... (see the link for more values)

Links

• Amiram Eldar, Table of n, a(n) for n = 1..559
• Amiram Eldar, Table of n, a(n), A048105(a(n)) for n = 1..559

Crossrefs

Cf. A048105, A002182 (highly composite), A002110 (unitary), A037992 (infinitary), A293185 (bi-unitary), A318278 (exponential).

Programs

Mathematica

f[n_] := DivisorSigma[0, n] - 2^PrimeNu[n]; fm=-1; s={}; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, n]], {n, 1, 10^5}]; s