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%I #37 Mar 08 2023 16:18:15
%S 33,85,93,121,141,170,201,213,217,244,284,301,393,428,434,445,506,602,
%T 603,604,633,637,697,841,921,962,1041,1074,1083,1084,1130,1137,1244,
%U 1261,1274,1309,1345,1401,1412,1430,1434,1448,1490,1532,1556,1586,1604
%N Numbers m such that the factorizations of m..m+2 have the same number of primes (including multiplicities).
%H Charles R Greathouse IV, <a href="/A045939/b045939.txt">Table of n, a(n) for n = 1..10000</a>
%t 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 *)
%t pd2Q[n_]:=PrimeOmega[n]==PrimeOmega[n+1]==PrimeOmega[n+2]; Select[Range[1700],pd2Q] (* _Harvey P. Dale_, Apr 19 2011 *)
%t SequencePosition[PrimeOmega[Range[1700]],{x_,x_,x_}][[;;,1]] (* _Harvey P. Dale_, Mar 08 2023 *)
%o (PARI) is(n)=my(t=bigomega(n)); bigomega(n+1)==t && bigomega(n+2)==t \\ _Charles R Greathouse IV_, Sep 14 2015
%o (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
%Y 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).
%Y A056809 is a subsequence.
%Y Cf. A006073. - _Harvey P. Dale_, Apr 19 2011
%K nonn,easy
%O 1,1
%A _David W. Wilson_
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