Last week Letsko Validimir added one new record to
the problem 20, which deals with
extending the following table: "Least set of K consecutive integers
having the same quantity d of divisors.
|
K |
Least
set |
d |
Source |
|
2 |
2 to 3
(and the only set) |
2 |
Anonymous |
|
3 |
33
to 35 |
4 |
R.
K. Guy |
|
4 |
242
to 245 |
6 |
R.
K. Guy |
|
5 |
11605
to 11609 (least)
40311 to
40315 (not least) |
8
8 |
C.
Rivera
R. K. Guy |
|
6 |
28374
to 28379 |
8 |
C.
Rivera |
|
7 |
171893
to 171899 |
8
|
S.
Vandemergel, 1987 |
|
8 |
1043710445721 |
48 |
Jud Mc Cranie, 2002 |
|
9 |
17796126877482329126044
to
17796126877482329126052 “presumably not the
smallest of this kind", says Guy |
48 |
Düntsch
& Eggleton, 1990 |
|
10 |
Start at 14366256627859031643
(Least?) |
24 |
Bruno Mishutka and Bilgin |
|
11 |
Start at 193729158984658237901148
(Least?) |
48 |
Bruno Mishutka and Bilgin |
|
12 |
Start at
1284696910355238430481207644 (Least?) |
24 |
Bruno Mishutka and Bilgin |
|
13 |
Start at
58032555961853414629544105797569 (Least?) |
24 |
Letsko Vladimir |
For K<=9, See R. K. Guy's
"Unsolved Problems in Number Theory", 2nd edition, B18, p. 73.
For K=8 and K>9 see Problem 20.
Q1. Are these the least
solutions for K=9. 10, 11, 12 and 13?
Q2 Find solutions for K>13
