tau(k)/bigomega(k)
Emeric Deutsch
deutsch at duke.poly.edu
Wed Jun 29 16:23:15 CEST 2005
Dear Seqfans,
Sequence A109421 gives the numbers k such that tau(k)/bigomega(k)
is an integer [tau(k)=number of divisors of k; bigomega(k)=number
of prime divisors of k, counted with multiplicities].
My question: does the set {tau(k)/bigomega(k): k=2,3,...} contain
all integers n>=2?
We (= Maple and I) have found that the least k such that
tau(k)/bigomega(k)=n is given by the table:
n k
- -
2 2
3 60
4 210
5 2160
6 1260
7 77760
8 4620
9 12600
10 18480
11 3456000
12 27720
13 4730880
14 302400
15 453600
16 120120
17 >11,000,000 if it exists
18 180180
19 >11,000,000 if it exists
20 997920
21 1108800
22 10644480
23 >11,000,000 if it exists
24 720720
25 2494800
26 >11,000,000 if it exists
27 3880800
28 2882880
29 >11,000,000 if it exists
30 5821200
31 >11,000,000 if it exists
32 3063060
33 >11,000,000 if it exists
34 >11,000,000 if it exists
35 >11,000,000 if it exists
36 7207200
37 >11,000,000 if it exists
38 >11,000,000 if it exists
39 >11,000,000 if it exists
40 10810800
I have similar questions and comparable data for A109423,A109425, and
A109427.
I'd appreciate collaborators.
Thanks.
Emeric
More information about the SeqFan
mailing list