A045940 Numbers m such that the factorizations of m..m+3 have the same number of primes (including multiplicities).

602, 603, 1083, 2012, 2091, 2522, 2523, 2524, 2634, 2763, 3243, 3355, 4023, 4202, 4203, 4921, 4922, 4923, 5034, 5035, 5132, 5203, 5282, 5283, 5785, 5882, 5954, 5972, 6092, 6212, 6476, 6962, 6985, 7314, 7730, 7731, 7945, 8393, 8825, 8956, 8972, 9162

Offset

1,1

Links

Zak Seidov and Michael De Vlieger, Table of n, a(n) for n = 1..11998 (First 3356 terms from Zak Seidov)

Mathematica

f[n_]:=Plus@@Last/@FactorInteger[n]; lst={}; lst={}; Do[If[f[n]==f[n+1]==f[n+2]==f[n+3], AppendTo[lst, n]], {n, 0, 8!}]; lst (* Vladimir Joseph Stephan Orlovsky, May 12 2010 *)
SequencePosition[PrimeOmega[Range[10000]], {x_, x_, x_, x_}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 02 2020 *)

Prog

(PARI) isok(n) = (bigomega(n) == bigomega(n+1)) && (bigomega(n+1) == bigomega(n+2)) && (bigomega(n+2) == bigomega(n+3)); \\ Michel Marcus, Jan 06 2015

Crossrefs

Numbers m through m+k have the same number of prime divisors (with multiplicity): A045920 (k=1), A045939 (k=2), this sequence (k=3), A045941 (k=4), A045942 (k=5), A123103 (k=6), A123201 (k=7), A358017 (k=8), A358018 (k=9), A358019 (k=10).

Cf. A045932 (similar, with omega).

Sequence in context: A292069 A107440 A218055 * A124057 A252435 A363830

Adjacent sequences: A045937 A045938 A045939 * A045941 A045942 A045943

Keyword

nonn

Author

David W. Wilson

Status

approved