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Numbers whose sum of distinct prime factors is 3-almost prime.
1

%I #18 Jan 22 2025 05:20:45

%S 15,35,42,45,51,65,75,77,78,84,86,91,110,115,122,123,126,130,135,138,

%T 141,146,153,154,156,161,168,172,175,185,187,194,201,206,209,219,220,

%U 221,222,225,230,234,235,244,245,252,259,260,266,267,276,282,285,292

%N Numbers whose sum of distinct prime factors is 3-almost prime.

%C Numbers k such that A008472(k) is an element of A014612.

%C This is the 3-almost prime analog of A114522.

%H Charles R Greathouse IV, <a href="/A114988/b114988.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 15 because 15 = 3 * 5 and 3 + 5 = 8 = 2^3 is a 3-almost prime.

%e a(2) = 35 because 15 = 5 * 7 and 5 + 7 = 12 = 2^2 * 3 is a 3-almost prime.

%e a(3) = 42 because 42 = 2 * 3 * 7 and 2 + 3 + 7 = 12 = 2^2 * 3 is a 3-almost prime.

%e a(4) = 45 because 45 = 3^2 * 5 and 3 + 5 = 8 = 2^3 is a 3-almost prime.

%e a(5) = 51 because 51 = 3 * 17 and 3 + 17 = 20 = 2^2 * 5 is a 3-almost prime.

%e a(6) = 65 because 65 = 5 * 13 and 5 + 13 = 18 = 2 * 3^2 is a 3-almost prime.

%t Select[Range[1000], PrimeOmega[ Total[ First /@ FactorInteger[#]]] == 3 &] (* _Giovanni Resta_, Jun 15 2016 *)

%o (PARI) is(n)=bigomega(vecsum(factor(n)[,1]))==3 \\ _Charles R Greathouse IV_, Feb 05 2017

%Y Cf. A008472, A014612, A114522.

%K easy,nonn,changed

%O 1,1

%A _Jonathan Vos Post_, Feb 22 2006

%E Corrected and extended by _Giovanni Resta_, Jun 15 2016