A309141 - OEIS

%I #14 Apr 10 2020 14:55:53

%S 1,4,8,16,24,36,48,72,144,216,288,360,576,720,1080,1440,2160,2880,

%T 3600,4320,5040,7200,7560,10080,15120,20160,25200,30240,45360,50400,

%U 60480,75600,100800,110880,151200,221760,277200,302400,332640,453600,498960,554400,665280

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

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

%C 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)

%H Amiram Eldar, <a href="/A309141/b309141.txt">Table of n, a(n) for n = 1..559</a>

%H Amiram Eldar, <a href="/A309141/a309141.txt">Table of n, a(n), A048105(a(n)) for n = 1..559</a>

%t 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

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

%K nonn

%O 1,2

%A _Amiram Eldar_, Jul 14 2019