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 A180117 Numbers n such that n and n+2 are both divisible by exactly 3 primes (counted with multiplicity). 4

%I

%S 18,28,42,50,66,68,76,114,170,172,186,188,236,242,244,266,273,282,284,

%T 290,316,343,354,385,402,404,410,423,426,428,434,436,475,506,596,602,

%U 603,604,637,652,663,668,722,762,775,786,788,845,890,892,906,925,962

%N Numbers n such that n and n+2 are both divisible by exactly 3 primes (counted with multiplicity).

%C "Triprimes" or "3-almost primes" that keep that property when incremented by 2. Note that we don't care whether m+1 is also divisible by exactly 3 primes, as we first see with the triple (170, 171, 172). This sequence is to 3 as A092207 is to 2 and as A001359 is to 1. That is, this sequence is the 3rd row of the infinite array A[k,n] = n-th natural number m such that m and m+2 are both divisible by exactly k primes (counted with multiplicity). The first row is the lesser of twin primes. The second row is the sequence such that m and m+2 are both semiprimes.

%H Harvey P. Dale, <a href="/A180117/b180117.txt">Table of n, a(n) for n = 1..1000</a>

%F {i such that i in A014612 and i+2 i in A014612}.

%e a(1) = 18 because 18 = 2*3*3 and 18+2 = 20 = 2*2*5 both have 3 prime divisors, counted with multiplicity.

%e a(2) = 28 because 28 = 2*2*7 and 28+2 = 30 = 2*3*5 both have 3 prime divisors, counted with multiplicity.

%t #[[1,1]]&/@(Select[Partition[Table[{n,PrimeOmega[n]},{n,1000}],3,1], #[[1,2]]==#[[3,2]]==3&]) (* _Harvey P. Dale_, Oct 20 2011 *)

%t SequencePosition[PrimeOmega[Range[1000]],{3,_,3}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Apr 08 2017 *)

%o (PARI) is(n)=bigomega(n)==3 && bigomega(n+2)==3 \\ _Charles R Greathouse IV_, Jan 31 2017

%Y Cf. A001359, A014612.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Aug 10 2010

%E More terms from _R. J. Mathar_, Aug 13 2010

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