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%I #11 Feb 05 2017 02:37:44
%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 This is the 3-almost prime analog of A114522 "numbers n such that sum of distinct prime divisors of n is prime."
%H Charles R Greathouse IV, <a href="/A114988/b114988.txt">Table of n, a(n) for n = 1..10000</a>
%F {k such that A008472(k) is an element of A014612}. {k such that sopf(k) is an element of A014612}. {k = Product(Prime(j)^e_j) such that Sum(Prime(j)) is in A014612}. {k such that A008472(k) is an element of Union[8-almost primes (A014613), 12-almost primes (A069273), 18-almost primes (A069279), 20-almost primes (A069281), 27-almost primes]...
%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, A014613, A069273, A069279, A069281, A114522.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Feb 22 2006
%E Corrected and extended by _Giovanni Resta_, Jun 15 2016
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