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

Author

David W. Wilson

Keywords

• nonn
• easy

Links

• Charles R Greathouse IV, 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), 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

Programs

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 *)

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