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

Offset: 1

Author

Jonathan Vos Post, Feb 22 2006

Keywords

• easy
• nonn

Comments

Numbers k such that A008472(k) is an element of A014612.

This is the 3-almost prime analog of A114522.

Examples

			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.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008472, A014612, A114522.

Programs

Mathematica

Select[Range[1000], PrimeOmega[ Total[ First /@ FactorInteger[#]]] == 3 &] (* Giovanni Resta, Jun 15 2016 *)

PARI

is(n)=bigomega(vecsum(factor(n)[,1]))==3 \\ Charles R Greathouse IV, Feb 05 2017

Extensions

Corrected and extended by Giovanni Resta, Jun 15 2016