Almost Prime
A number 
with prime factorization
is called
-almost prime when the sum of the Powers 
. The set of -almost primesis denoted 
. The A000040). The2-almost prime numbers correspond to A001358).The first few 3-almost primes are 8, 12, 18, 20, 27, 28, 30, 42, 44, 45, 50, 52, 63, 66, 68, 70, 75, 76, 78, 92, 98, 99,... (Sloane's A014612). The first few 4-almost primes are 16, 24, 36, 40, 54, 56, 60, 81, 84, 88, 90, 100, ...(Sloane's A014613). The first few 5-almost primes are 32, 48, 72, 80, ... (Sloane's A014614).
See also Chen's Theorem, Prime Number, Semiprime
References
Sloane, N. J. A. Sequences A014612,A014613,A014614,A000040/M0652, andA001358/M3274in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.
- Phi Curve
- Phi Number System
- Phragmén-Lindêlöf Theorem
- Phyllotaxis
- Pi
- Piano Mover's Problem
- Picard's Existence Theorem
- Picard's Little Theorem
- Picard's Theorem
- Picard Variety
- Pick's Formula
- Pick's Theorem
- Picone's Theorem
- Piecewise Circular Curve
- Pie Cutting
- Pigeonhole Principle
- Pi Heptomino
- Pillai's Conjecture
- Pilot Vector
- Pinching Theorem
- Pinch Point
- Pine Cone Number
- Piriform
- Pisot-Vijayaraghavan Constants
- Pistol