A114988 - OEIS

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A114988

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

15, 35, 42, 45, 51, 65, 75, 77, 78, 84, 86, 91, 110, 115, 122, 123, 126, 130, 135, 138, 141, 146, 153, 154, 156, 161, 168, 172, 175, 185, 187, 194, 201, 206, 209, 219, 220, 221, 222, 225, 230, 234, 235, 244, 245, 252, 259, 260, 266, 267, 276, 282, 285, 292

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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