A365795 - OEIS

%I #17 Sep 30 2023 20:57:54

%S 30,60,70,90,120,140,150,180,240,270,280,286,300,350,360,450,480,490,

%T 540,560,572,600,646,700,720,750,810,900,960,980,1080,1120,1144,1200,

%U 1292,1350,1400,1440,1500,1620,1750,1798,1800,1920,1960,2160,2240,2250,2288,2400,2430,2450

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

%C The lower prime factor p_1 is equal to 2 and the other two are twin primes: p_3 - p_2 = 2.

%H Hugo Pfoertner, <a href="/A365795/b365795.txt">Table of n, a(n) for n = 1..10000</a>

%e 60 is a term since 60 = 2^2*3*5 and 2 + 3 = 5.

%e 286 is a term since 286 = 2*11*13 and 2 + 11 = 13.

%t Select[Range[2500],PrimeNu[#]==3&&Part[First/@FactorInteger[#],1]+Part[First/@FactorInteger[#],2]==Part[First/@FactorInteger[#],3]&]

%o (PARI) isok(k) = if (omega(k)==3, my(f=factor(k)[,1]); f[1] + f[2] == f[3]); \\ _Michel Marcus_, Sep 19 2023

%Y Cf. A001221, A001359, A006512, A071142.

%Y Subsequence of A033992 and of A071140.

%K nonn

%O 1,1

%A _Stefano Spezia_, Sep 19 2023