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