OFFSET
1,1
COMMENTS
This is the 3-almost prime analog of A114522 "numbers n such that sum of distinct prime divisors of n is prime."
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
{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]...
EXAMPLE
a(1) = 15 because 15 = 3 * 5 and 3 + 5 = 8 = 2^3 is a 3-almost prime.
a(2) = 35 because 15 = 5 * 7 and 5 + 7 = 12 = 2^2 * 3 is a 3-almost prime.
a(3) = 42 because 42 = 2 * 3 * 7 and 2 + 3 + 7 = 12 = 2^2 * 3 is a 3-almost prime.
a(4) = 45 because 45 = 3^2 * 5 and 3 + 5 = 8 = 2^3 is a 3-almost prime.
a(5) = 51 because 51 = 3 * 17 and 3 + 17 = 20 = 2^2 * 5 is a 3-almost prime.
a(6) = 65 because 65 = 5 * 13 and 5 + 13 = 18 = 2 * 3^2 is a 3-almost prime.
MATHEMATICA
Select[Range[1000], PrimeOmega[ Total[ First /@ FactorInteger[#]]] == 3 &] (* Giovanni Resta, Jun 15 2016 *)
PROG
(PARI) is(n)=bigomega(vecsum(factor(n)[, 1]))==3 \\ Charles R Greathouse IV, Feb 05 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 22 2006
EXTENSIONS
Corrected and extended by Giovanni Resta, Jun 15 2016
STATUS
approved