Problems & Puzzles: Problems

Problem 61. Problem 20 revisited

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 DŁntsch & 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


 


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