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A268588 Numbers n such that n, n + 1, n + 2, n + 3 and n + 4 are products of exactly three primes.

%I A268588 #17 Sep 08 2022 08:46:15
%S A268588 602,2522,2523,4202,4921,4922,5034,5282,7730,18241,18242,18571,19129,
%T A268588 21931,23161,23305,25203,25553,25554,27290,27291,29233,30354,30793,
%U A268588 32035,33843,34561,35714,36001,36835,40313,40314,40394,45265,55361,67609,69667,70202,72721
%N A268588 Numbers n such that n, n + 1, n + 2, n + 3 and n + 4 are products of exactly three primes.
%C A268588 Subsequence of A045941. - _Zak Seidov_, Jan 29 2017
%H A268588 Chai Wah Wu, <a href="/A268588/b268588.txt">Table of n, a(n) for n = 1..11023</a>
%e A268588 a(1) = 602: 602 = 2 * 7 * 43; 603 = 3 * 3 * 67; 604 = 2 * 2 * 151; 605 = 5 * 11 * 11; 606 = 2 * 3 * 101 are all products of three primes.
%e A268588 a(4) = 4202 : 4202 = 2 * 11 * 191; 4203 = 3 * 3 * 467; 4204 = 2 * 2 * 1051; 4205 = 5 * 29 * 29; 4206 = 2 * 3 * 701 are all products of three primes.
%p A268588 with(numtheory): A268588:= proc() if bigomega(n)=3 and bigomega(n+1)=3 and bigomega(n+2)=3 and bigomega(n+3)=3 and bigomega(n+4)=3 then RETURN (n); fi; end: seq(A268588(), n=1..100000);
%t A268588 Select[Range[100000], PrimeOmega[#] == 3 && PrimeOmega[# + 1] == 3 && PrimeOmega[# + 2] == 3 && PrimeOmega[# + 3] == 3 && PrimeOmega[# + 4] == 3 &]
%t A268588 SequencePosition[PrimeOmega[Range[73000]],{3,3,3,3,3}][[All,1]] (* _Harvey P. Dale_, Sep 03 2021 *)
%o A268588 (PARI) for(n = 1,50000, bigomega(n)==3 & bigomega(n+1)==3 & bigomega(n+2)==3 & bigomega(n+3)==3 & bigomega(n+4)==3 & print1(n,","))
%o A268588 (Magma) IsP3:=func< n | &+[k[2]: k in Factorization(n)] eq 3 >; [ n: n in [2..50000] | IsP3(n) and IsP3(n+1) and IsP3(n+2) and IsP3(n+3) and IsP3(n+4)];
%Y A268588 Cf. A056809, A113789, A124057, A045941.
%K A268588 nonn
%O A268588 1,1
%A A268588 _K. D. Bajpai_, Feb 07 2016
%E A268588 Comment removed by _Zak Seidov_, Jan 29 2017