A088983 -id:A088983 - cp's OEIS frontend

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

David W. Wilson

nonn

			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.

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.

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

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

A088986 Numbers k such that each of k through k+4 are divisible by exactly two primes.

Original entry on oeis.org

54, 91, 92, 115, 141, 142, 143, 144, 158, 205, 212, 213, 214, 215, 295, 301, 323, 324, 325, 391, 535, 685, 721, 799, 1135, 1345, 1465, 1535, 1711, 1941, 1981, 2101, 2215, 2302, 2303, 2304, 2425, 2641, 3865, 4411, 5461, 6505, 6625, 6925, 7165, 7231, 7261

Offset: 1

Labos Elemer, Sep 30 2003

nonn

Identical with A045933 from first-to 38th terms, but deviates later because A045933 includes start of chains with more than 2 prime-factors.
Contrary to longer chains (6, 7, 8, ...) of omega = 2 this sequence seems to be either infinite or very long. See comments in A088983 [especially Eggleton via Kimberley, 2017].
Primes counted without multiplicity. - Harvey P. Dale, Oct 20 2011

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..750 from Harvey P. Dale)

Cf. A001221, A045933, A088983.

Transpose[Select[Partition[Transpose[Select[Table[{n,PrimeNu[n]},{n,10000}],Last[#]==2&]][[1]],5,1],Last[#]-First[#]==4&]][[1]] (* Harvey P. Dale, Oct 20 2011 *)

lista(kmax) = {my(q = vector(5)); for(k = 6, kmax, q = concat(vecextract(q, "^1"), omega(k) == 2); if(vecmin(q) == 1, print1(k-4, ", ")));} \\ Amiram Eldar, Jul 11 2024

from sympy import primefactors
def ok(n):
    return all(len(primefactors(n + i))==2 for i in range(5))
print([n for n in range(1, 8001) if ok(n)]) # Indranil Ghosh, Jul 17 2017

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

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