This site is supported by donations to The OEIS Foundation.

Compositorial

From OeisWiki
Jump to: navigation, search


This article needs more work.

Please help by expanding it!


The th compositorial number, denoted , is defined as the product of the first composites, the 0th compositorial number being the empty product, defined as the multiplicative identity, i.e. 1.

The compositorial of a natural number , denoted , is the product of all positive composite integers up to , the compositorial of 0 being the empty product, defined as the multiplicative identity, i.e. 1.

Formulae

Formulae for composite numbers

The th compositorial number is given by

where is the th composite number.

Formulae for natural numbers

The compositorial of is given by

where is the factorial of and is the primorial of .

The compositorial of is the quotient of by the squarefree kernel (or radical ) of

Sequences

A036691 The compositorial numbers, .

{1, 4, 24, 192, 1728, 17280, 207360, 2903040, 43545600, 696729600, 12541132800, 250822656000, 5267275776000, 115880067072000, 2781121609728000, 69528040243200000, 1807729046323200000, ...}

The compositorial of , i.e. . (A049614, )

{1, 1, 1, 1, 4, 4, 24, 24, 192, 1728, 17280, 17280, 207360, 207360, 2903040, 43545600, 696729600, 696729600, 12541132800, 12541132800, 250822656000, 5267275776000, 115880067072000, ...}

See also