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

1,1

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.

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A020301 A083517 A088983 * A051347 A293647 A225908

Adjacent sequences: A045931 A045932 A045933 * A045935 A045936 A045937

Keyword

nonn

Author

David W. Wilson

Status

approved