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%I #15 Jan 05 2020 05:54:52
%S 270,592,700,750,918,1168,1240,1638,1648,1672,1710,1750,2070,2310,
%T 2392,2548,2550,2608,2728,2860,2862,2896,2898,3184,3330,3568,3630,
%U 3822,3848,3850,3942,3976,4230,4264,4648,4662,5070,5080,5236,5238,5390,5550,5560
%N Numbers k such that k and k + 2 are both divisible by exactly five primes (counted with multiplicity).
%C "5-almost primes" that keep that property when incremented by 2. This sequence is to 5 as 4 is to A180150, as 3 is to A180117, as A092207 is to 2, and as A001359 is to 1. That is, this sequence is the 5th 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 Amiram Eldar, <a href="/A180151/b180151.txt">Table of n, a(n) for n = 1..10000</a>
%F {m in A014614 and m+2 in A014614} = {m such that bigomega(m) = bigomega(m+2) = 5} = {m such that A001222(m) = A001222(m+2) = 5}.
%e a(1) = 270 because 270 = 2 * 3^3 * 5 is divisible by exactly 5 primes (counted with multiplicity), and so is 270+2 = 272 = 2^4 * 17.
%t f[n_] := Plus @@ (Last@# & /@ FactorInteger@n); fQ[n_] := f[n] == 5 == f[n + 2]; Select[ Range@ 10000, fQ] (* _Robert G. Wilson v_, Aug 15 2010 *)
%o (PARI) for(x=2,10^4,if(bigomega(x)==5&&bigomega(x+2)==5,print1(x", "))) \\ _Zak Seidov_, Aug 12 2010
%Y Cf. A000040, A001222, A001358, A001359, A014614, A033987, A101637, A180117, A180150.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Aug 12 2010
%E Corrected and extended by _Zak Seidov_ and _R. J. Mathar_, Aug 12 2010
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