Smooth number

In number theory, a smooth (or friable) number is an integer which factors completely into small prime numbers. The term seems to have been coined by Leonard Adleman. Smooth numbers are especially important in cryptography relying on factorization. The 2-smooth numbers are just the powers of 2.

Definition

A positive integer is called B-smooth if none of its prime factors is greater than B. For example, 1,620 has prime factorization 2² × 3⁴ × 5; therefore 1,620 is 5-smooth because none of its prime factors are greater than 5. This definition includes numbers that lack some of the smaller prime factors; for example, both 10 and 12 are 5-smooth, despite the fact that they miss out prime factors 3 and 5 respectively. 5-smooth numbers are also called regular numbers or Hamming numbers; 7-smooth numbers are also called humble, and sometimes called highly composite, although this conflicts with another meaning of highly composite numbers.

Note that B does not have to be a prime factor. If the largest prime factor of a number is p then the number is B-smooth for any B ≥ p. Usually B is given as a prime, but composite numbers work as well. A number is B-smooth if and only if it is p-smooth, where p is the largest prime less than or equal to B.

Smooth jazz

Smooth jazz is a genre of music that grew out of jazz and is influenced by rhythm and blues, funk, rock and roll, and pop music styles (separately, or, in any combination). Musicians such as Kenny G., Ramsey Lewis, David Koz, and Spyro Gyra have had hits with instrumental recordings, while singers such as Anita Baker, Sade, Sting and Norah Jones have found success with vocal releases. George Benson remains a popular Smooth Jazz artist as both a singer and guitar player.

Smooth jazz was once successful as a radio format. However, in 2007, the popularity of the format began to slide. Consequently, it was abandoned by several high-profile radio stations across the U.S.A., including WQCD (now WFAN-FM) in New York, WNUA Chicago (now WEBG), WJJZ in Philadelphia (now WISX), and KKSF (now KOSF) in San Francisco. Programmers say the audience for the format has aged beyond the prime demographic sought by advertisers. Despite the format's demise outside a handful of commercial radio outlets, a number of non-commercial and HD stations have taken up the music. It is still available on SiriusXM on Channel 66, known as "Watercolors" and on the Music Choice cable radio service. In addition, smooth jazz concerts, recording sales, as well as increased smooth jazz offerings on the Internet, continue to show strong fan support for the genre.

Smooth

Smooth means having a texture that lacks friction. It is the opposite of rough.

Smooth may also refer to:

In mathematics

In entertainment

Other uses

See also

Smooth Criminal

"Smooth Criminal" is the seventh single from American recording artist Michael Jackson's 1987 Bad album. The song contains a fast-paced beat intertwined with Jackson's lyrics about a woman named Annie, who has been violently attacked in her apartment by a "smooth" assailant. First broadcast on television as a video in early October, it was released as a single on October 21, 1988, and peaked at number seven on the Billboard Hot 100. It was re-released on April 10, 2006, as a part of the Visionary: The Video Singles box set. The re-released Visionary single charted at number 19 in the UK. The piece is one of Jackson's signature songs, and has appeared on numerous greatest hits albums, including Number Ones, The Essential Michael Jackson, Michael Jackson: The Ultimate Collection, King of Pop, This Is It, and Immortal.

The song serves as the theme song to Jackson's 1988 film Moonwalker, and plays as the background soundtrack in a section of the video game Michael Jackson's Moonwalker.

Michael Jackson

Michael Joseph Jackson (August 29, 1958 – June 25, 2009) was an American singer, songwriter, record producer, dancer, and actor. Called the King of Pop, his contributions to music and dance, along with his publicized personal life, made him a global figure in popular culture for over four decades.

The eighth child of the Jackson family, he debuted on the professional music scene along with his elder brothers Jackie, Tito, Jermaine, and Marlon as a member of the Jackson 5 in 1964, and began his solo career in 1971. In the early 1980s, Jackson became a dominant figure in popular music. The music videos for his songs, including those of "Beat It", "Billie Jean", and "Thriller" from his 1982 album Thriller, were credited with breaking down racial barriers and with transforming the medium into an art form and promotional tool. The popularity of these videos helped to bring the then-relatively-new television channel MTV to fame. His 1987 album Bad spawned the U.S. Billboard Hot 100 number-one singles "I Just Can't Stop Loving You", "Bad", "The Way You Make Me Feel", "Man in the Mirror", and "Dirty Diana", becoming the first album to have five number-one singles on the Billboard Hot 100. With videos such as "Black or White" and "Scream", he continued to innovate the medium throughout the 1990s, as well as forging a reputation as a touring solo artist. Through stage and video performances, Jackson popularized a number of complicated dance techniques, such as the robot and the moonwalk, to which he gave the name. His distinctive sound and style has influenced numerous artists of various music genres.