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A114988
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Numbers whose sum of distinct prime factors is 3-almost prime.
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0
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15, 35, 42, 45, 51, 65, 75, 77, 78, 84, 86, 91, 110, 115, 123
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This is the 3-almost prime analogue of A114522 "numbers n such that sum of distinct prime divisors of n is prime."
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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]...
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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.
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CROSSREFS
| Cf. A008472, A014612, A014613, A069273, A069279, A069281, A114522.
Sequence in context: A202237 A080774 A146319 * A130871 A143202 A108668
Adjacent sequences: A114985 A114986 A114987 * A114989 A114990 A114991
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 22 2006
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