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A365795 Numbers k such that omega(k) = 3 and its prime factors satisfy the equation p_1 + p_2 = p_3.

%I A365795 #17 Sep 30 2023 20:57:54
%S A365795 30,60,70,90,120,140,150,180,240,270,280,286,300,350,360,450,480,490,
%T A365795 540,560,572,600,646,700,720,750,810,900,960,980,1080,1120,1144,1200,
%U A365795 1292,1350,1400,1440,1500,1620,1750,1798,1800,1920,1960,2160,2240,2250,2288,2400,2430,2450
%N A365795 Numbers k such that omega(k) = 3 and its prime factors satisfy the equation p_1 + p_2 = p_3.
%C A365795 The lower prime factor p_1 is equal to 2 and the other two are twin primes: p_3 - p_2 = 2.
%H A365795 Hugo Pfoertner, <a href="/A365795/b365795.txt">Table of n, a(n) for n = 1..10000</a>
%e A365795 60 is a term since 60 = 2^2*3*5 and 2 + 3 = 5.
%e A365795 286 is a term since 286 = 2*11*13 and 2 + 11 = 13.
%t A365795 Select[Range[2500],PrimeNu[#]==3&&Part[First/@FactorInteger[#],1]+Part[First/@FactorInteger[#],2]==Part[First/@FactorInteger[#],3]&]
%o A365795 (PARI) isok(k) = if (omega(k)==3, my(f=factor(k)[,1]); f[1] + f[2] == f[3]); \\ _Michel Marcus_, Sep 19 2023
%Y A365795 Cf. A001221, A001359, A006512, A071142.
%Y A365795 Subsequence of A033992 and of A071140.
%K A365795 nonn
%O A365795 1,1
%A A365795 _Stefano Spezia_, Sep 19 2023