

A365795


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


1



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
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OFFSET

1,1


COMMENTS

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


LINKS



EXAMPLE

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.


MATHEMATICA

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


PROG

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


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



