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A114988 Numbers whose sum of distinct prime factors is 3-almost prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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

Cf. A008472, A014612, A014613, A069273, A069279, A069281, A114522.

Sequence in context: A146319 A238605 A233561 * A130871 A332378 A244969

Adjacent sequences: A114985 A114986 A114987 * A114989 A114990 A114991

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Feb 22 2006

EXTENSIONS

Corrected and extended by Giovanni Resta, Jun 15 2016

STATUS

approved

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Last modified January 30 05:55 EST 2023. Contains 359939 sequences. (Running on oeis4.)