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Numbers with relatively many divisors

Definition

The number ${\displaystyle \scriptstyle n\,}$ is in the sequence iff

${\displaystyle \tau (n)\geq max(\tau (1),\ldots ,\tau (n-1))-1,\,}$

where tau(n) is the number of divisors of n.

This definition gives the sequence (A??????) which is not yet in the OEIS

{2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 24, 30, 36, 40, 42, 48, 60, 72, 84, 90, 96, 108, 120, ...

Table giving the above sequence (Cf. A000005 for tau(n))

n            tau(n)    tau(n) - max[tau(1), ... tau(n-1)]

1	 	1
2		2	 	+1
3		2	 	 0
4		3	 	+1
5		2	 	-1
6		4	 	+1
7		2
8		4	 	 0
9		3	 	-1
10		4	 	 0
11		2
12		6	 	+2
13		2
14		4
15		4
16		5	 	-1
17		2
18		6	 	 0
19		2
20		6	 	 0
21		4
22		4
23		2
24		8	 	+2
25		3
26		4
27		4
28		6
29		2
30		8	 	 0
31		2
32		6
33		4
34		4
35		4
36		9	 	+1
37		2
38		4
39		4
40		8	 	-1
41		2
42		8	 	-1
43		2
44		6
45		6
46		4
47		2
48		10	 	+1
49		3
50		6
51		4
52		6
53		2
54		8
55		4
56		8
57		4
58		4
59		2
60		12	 	+2
61		2
62		4
63		6
64		7
65		4
66		8
67		2
68		6
69		4
70		8
71		2
72		12	 	 0
73		2
74		4
75		6
76		6
77		4
78		8
79		2
80		10
81		5
82		4
83		2
84		12	 	 0
85		4
86		4
87		4
88		8
89		2
90		12	 	 0
91		4
92		6
93		4
94		4
95		4
96		12	 	 0
97		2
98		6
99		6
100		9
101		2
102		8
103		2
104		8
105             8
106 		4
107 		2
108 		12	 	 0
109 		2
110 		8
111 		4
112 		10
113 		2
114 		8
115 		4
116 		6
117 		6
118 		4
119 		4
120 		16		+4


Table of interesting bases (with relatively many divisors)

Interesting bases (with relatively many divisors)
Base Sequence OEIS

number

Formula
2
3
4
5
6
8
9
10
12
16
18
20
24
30
36
40
42
48
60
72
84
90
96
108
120