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

30, 60, 70, 90, 120, 140, 150, 180, 240, 270, 280, 286, 300, 350, 360, 450, 480, 490, 540, 560, 572, 600, 646, 700, 720, 750, 810, 900, 960, 980, 1080, 1120, 1144, 1200, 1292, 1350, 1400, 1440, 1500, 1620, 1750, 1798, 1800, 1920, 1960, 2160, 2240, 2250, 2288, 2400, 2430, 2450

Offset: 1

Author

Stefano Spezia, Sep 19 2023

Keywords

• nonn

Comments

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

Examples

			60 is a term since 60 = 2^2*3*5 and 2 + 3 = 5.
286 is a term since 286 = 2*11*13 and 2 + 11 = 13.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A001359, A006512, A071142.

Subsequence of A033992 and of A071140.

Programs

Mathematica

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

PARI

isok(k) = if (omega(k)==3, my(f=factor(k)[,1]); f[1] + f[2] == f[3]); \\ Michel Marcus, Sep 19 2023