A045934 Numbers n such that n through n+5 have the same number of distinct prime factors.

91, 141, 142, 143, 212, 213, 214, 323, 324, 2302, 2303, 6850, 9061, 10280, 10281, 15740, 16130, 16164, 16682, 16683, 19052, 19053, 20212, 20213, 21195, 21196, 21790, 22055, 23064, 25779, 25780, 25991, 28608, 28674, 29971, 31442, 33084

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Examples

			The numbers from 91 to 96 all have 2 distinct prime factors: 91=7*13, 92=2^2*23, 93=3*31, 94=2*47, 95=5*19, and 96=2^5*3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2620 from Zak Seidov)
• Roger B. Eggleton and James A. MacDougall, Consecutive integers with equally many principal divisors, Math. Mag. 81 (2008), 235-248.

Crossrefs

Cf. A001221, A006049, A006073, A045932-A045933, A045935-A045938, A088983.

Programs

Mathematica

Select[Range[35000],Length[Union[Length/@FactorInteger[Range[#,#+5]]]]==1&]  (* Harvey P. Dale, Feb 27 2011 *)