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A045939 Numbers n such that factorizations of n through n+2 have the same number of primes (including multiplicities). 12
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

A056809 is a subsequence.

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

Subsequence of A045920. _Zak Seidov, Jul 02 2020

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

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Last modified January 23 20:39 EST 2021. Contains 340386 sequences. (Running on oeis4.)