A045941 Numbers m such that the factorizations of m..m+4 have the same number of primes (including multiplicities).

602, 2522, 2523, 4202, 4921, 4922, 5034, 5282, 7730, 12122, 18241, 18242, 18571, 19129, 21931, 23161, 23305, 25203, 25553, 25554, 27290, 27291, 29233, 30354, 30793, 32035, 33843, 34561, 35124, 35714, 36001, 36835, 40313, 40314, 40394, 42182, 45265, 52854

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Links

• Donovan Johnson, Table of n, a(n) for n = 1..10000

Crossrefs

Numbers m through m+k have the same number of prime divisors (with multiplicity): A045920 (k=1), A045939 (k=2), A045940 (k=3), this sequence (k=4), A045942 (k=5), A123103 (k=6), A123201 (k=7), A358017 (k=8), A358018 (k=9), A358019 (k=10).

Programs

Mathematica

f[n_]:=Plus@@Last/@FactorInteger[n];lst={};lst={};Do[If[f[n]==f[n+1]==f[n+2]==f[n+3]==f[n+4],AppendTo[lst,n]],{n,0,9!}];lst (* Vladimir Joseph Stephan Orlovsky, May 12 2010 *)
Flatten[Position[Partition[Table[PrimeOmega[n],{n,55000}],5,1],?(Length[ Union[#]]==1&),{1},Heads->False]] (* _Harvey P. Dale, Nov 29 2015 *)