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A309141
Nonunitary highly composite numbers: numbers with a record number of nonunitary divisors.
12
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
1,2
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)
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
CROSSREFS
Cf. A048105, A002182 (highly composite), A002110 (unitary), A037992 (infinitary), A293185 (bi-unitary), A318278 (exponential).
Sequence in context: A355392 A290498 A137932 * A329882 A309181 A140466
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 14 2019
STATUS
approved