A045939 Numbers m such that the factorizations of m..m+2 have the same number of primes (including multiplicities).

33, 85, 93, 121, 141, 170, 201, 213, 217, 244, 284, 301, 393, 428, 434, 445, 506, 602, 603, 604, 633, 637, 697, 841, 921, 962, 1041, 1074, 1083, 1084, 1130, 1137, 1244, 1261, 1274, 1309, 1345, 1401, 1412, 1430, 1434, 1448, 1490, 1532, 1556, 1586, 1604

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Mathematica

f[n_]:=Plus@@Last/@FactorInteger[n]; lst={}; lst={}; Do[If[f[n]==f[n+1]==f[n+2], AppendTo[lst, n]], {n, 0, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, May 12 2010 *)
pd2Q[n_]:=PrimeOmega[n]==PrimeOmega[n+1]==PrimeOmega[n+2]; Select[Range[1700], pd2Q]  (* Harvey P. Dale, Apr 19 2011 *)
SequencePosition[PrimeOmega[Range[1700]], {x_, x_, x_}][[;; , 1]] (* Harvey P. Dale, Mar 08 2023 *)

Prog

(PARI) is(n)=my(t=bigomega(n)); bigomega(n+1)==t && bigomega(n+2)==t \\ Charles R Greathouse IV, Sep 14 2015
(PARI) list(lim)=my(v=List(), a=1, b=1, c); forfactored(n=4, lim\1+2, c=bigomega(n); if(a==b&&a==c, listput(v, n[1]-2)); a=b; b=c); Vec(v) \\ Charles R Greathouse IV, May 07 2020

Crossrefs

Numbers m through m+k have the same number of prime divisors (with multiplicity): A045920 (k=1), this sequence (k=2), A045940 (k=3), A045941 (k=4), A045942 (k=5), A123103 (k=6), A123201 (k=7), A358017 (k=8), A358018 (k=9), A358019 (k=10).

A056809 is a subsequence.

Cf. A006073. - Harvey P. Dale, Apr 19 2011

Sequence in context: A094846 A044171 A044552 * A056809 A073251 A005238

Adjacent sequences: A045936 A045937 A045938 * A045940 A045941 A045942

Keyword

nonn,easy

Author

David W. Wilson

Status

approved