aarjaneiro/planetmath huggingface dataset:
totative

totative

Given a

positive integer

n

, an

integer

0

<

m

<

n

is a

totative

of

n

if

gcd

⁡

(

m

,

n

)

=

1

. Put another way, all the smaller integers than

n

that are

coprime

to

n

are totatives of

n

.

For example, the totatives of 21 are 1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19 and 20.

The count of totatives of

n

is Euler’s

totient function

ϕ

⁢

(

n

)

. The set of totatives of

n

forms a

reduced residue system

modulo

n

. The word “totative” was coined by

James Joseph Sylvester

, who also coined “

totient

” (though despite occasional usage in some papers and books, the term “totative” has not caught on the way “totient” has).

Title

totative

Canonical name

Totative

Date of creation

2013-03-22 16:58:16

Last modified on

2013-03-22 16:58:16

Owner

CompositeFan (12809)

Last modified by

CompositeFan (12809)

Numerical id

9

Author

CompositeFan (12809)

Entry type

Definition

Classification

msc 11A25

Related topic

ResidueSystems

Generated on Fri Feb 9 15:15:24 2018 by

LaTeXML
totient

totient

A

totient

is a

sequence

f

:

{

1

,

2

,

3

,

…

}

→

ℂ

such
that

g

∗

f

=

h

for some two

completely multiplicative

sequences

g

and

h

, where

∗

denotes the

convolution product

(or Dirichlet product; see

multiplicative function

).

The term ‘totient’ was introduced by Sylvester in the 1880’s, but is
seldom used nowadays except in two cases. The

Euler totient

ϕ

satisfies

ι

0

∗

ϕ

=

ι

1

where

ι

k

denotes the

function

n

↦

n

k

(which is completely
multiplicative). The more general

Jordan totient

J

k

is defined by

ι

0

∗

J

k

=

ι

k

.

Title

totient

Canonical name

Totient

Date of creation

2013-03-22 13:38:35

Last modified on

2013-03-22 13:38:35

Owner

mathcam (2727)

Last modified by

mathcam (2727)

Numerical id

5

Author

mathcam (2727)

Entry type

Definition

Classification

msc 11A25

Defines

totient

Defines

Jordan totient

Generated on Fri Feb 9 15:15:26 2018 by

LaTeXML
totient valence function

totient valence function

Given an

integer

n

, count how many integers

m

in the set

{

n

+

1

,

n

+

2

,

…

⁢

n

2

}

satisfy

ϕ

⁢

(

m

)

=

n

. This is the

totient

valence

of

n

, usually labelled

N

ϕ

⁢

(

n

)

. (The only two special cases are 2 and 6, for which one has to look a little beyound

n

2

).

Robert Carmichael conjectured that

N

ϕ

⁢

(

n

)

=

1

never. Two

sequences

in Sloane’s OEIS that list numbers with higher totient valences than preceding numbers are A007374 and A097942.

Title

totient valence function

Canonical name

TotientValenceFunction

Date of creation

2013-03-22 15:50:57

Last modified on

2013-03-22 15:50:57

Owner

CompositeFan (12809)

Last modified by

CompositeFan (12809)

Numerical id

5

Author

CompositeFan (12809)

Entry type

Definition

Classification

msc 11A25

Generated on Fri Feb 9 15:15:27 2018 by

LaTeXML
triangular number counting function

triangular number counting function

For a given nonnegative number

x

, the

triangular number counting function

counts how many

triangular numbers

are not greater than

x

. The formula is simple:

⌊

-

1

+

8

⁢

x

+

1

2

⌋

,

in sharp contrast to the lack of a formula for the

prime counting function

π

⁢

(

x

)

. If one accepts 0 as a triangular number, the formula easily accommodates this by the mere

addition

of 1 after flooring the

fraction

.

References

1

Zhi-Wei Sun, “On Sums of Primes and Triangular Numbers” ArXiv preprint, 10 April (2008): 1

Title

triangular number counting function

Canonical name

TriangularNumberCountingFunction

Date of creation

2013-03-22 18:03:03

Last modified on

2013-03-22 18:03:03

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 11A25

Generated on Fri Feb 9 15:15:29 2018 by

LaTeXML
uniqueness of Moebius function

uniqueness of Moebius function

Here is a sample result for the

function

, essentially classifying its uniqueness :

Proposition

1:

μ

is the unique

mapping

ℕ

*

→

ℤ

such that

μ

⁢

(

1

)

=

1

(1)

∑

d

|

n

μ

⁢

(

d

)

=

0

⁢

for all

⁢

n

>

1

(2)

Proof:

By

induction

, there can only be one function with these

properties

.

μ

clearly

satisfies

(1), so take some

n

>

1

. Let

p

be
some

prime factor

of

n

, and let

m

be the

product

of all the prime
factors of

n

.

∑

d

|

n

μ

⁢

(

d

)

=

∑

d

|

m

μ

⁢

(

d

)

=

∑

d

|

m

p

∤

d

μ

⁢

(

d

)

+

∑

d

|

m

p

∣

d

μ

⁢

(

d

)

=

∑

d

|

m

/

p

μ

⁢

(

d

)

-

∑

d

|

m

/

p

μ

⁢

(

d

)

=

0

Title

uniqueness of Moebius function

Canonical

name

UniquenessOfMoebiusFunction

Date of creation

2013-03-22 14:17:25

Last modified on

2013-03-22 14:17:25

Owner

mathcam (2727)

Last modified by

mathcam (2727)

Numerical id

6

Author

mathcam (2727)

Entry type

Definition

Classification

msc 11A25

Generated on Fri Feb 9 15:15:31 2018 by

LaTeXML
Wilson’s theorem

Wilson’s theorem

Wilson’s theorem states that

(

p

-

1

)

!

≡

-

1

(

mod

p

)

iff

p

is prime (note that it must be

positive

).

Title

Wilson’s theorem

Canonical name

WilsonsTheorem

Date of creation

2013-03-22 11:42:24

Last modified on

2013-03-22 11:42:24

Owner

CWoo (3771)

Last modified by

CWoo (3771)

Numerical id

33

Author

CWoo (3771)

Entry type

Theorem

Classification

msc 11A25

Classification

msc 37-01

Classification

msc 11-00

Synonym

Wilson-Lagrange theorem

Related topic

RuizIdentity

Related topic

PolynomialCongruence

Generated on Fri Feb 9 15:15:37 2018 by

LaTeXML
Zeisel number

Zeisel number

Given a

squarefree

integer

n

=

∏

i

=

0

ω

⁢

(

n

)

p

i

,

with

ω

⁢

(

n

)

>

2

(in which

ω

⁢

(

n

)

is

number of distinct prime factors function

, and all the

p

i

are

prime divisors

of

n

, except

p

0

=

1

purely as a notational convenience, and are sorted in

ascending order

) if each prime

p

i

fits into the

recurrence relation

p

i

=

m

⁢

p

i

-

1

+

a

, with

m

being some fixed integer multiplicand, and

a

being some fixed integer addend, then

n

is called a

Zeisel number

.

For example,

1419

=

1

×

3

×

11

×

43

. Say that

m

=

4

and

a

=

-

1

. This checks out:

3

=

m

+

a

,

11

=

3

⁢

m

+

a

and

43

=

11

⁢

m

+

a

. 1419 is a Zeisel number. The first few Zeisel numbers are 105, 1419, 1729, 1885, 4505, 5719, … listed in A051015 of Sloane’s OEIS. The

Carmichael numbers

of the form

(

6

⁢

n

+

1

)

⁢

(

12

⁢

n

+

1

)

⁢

(

18

⁢

n

+

1

)

are a subset of the Zeisel numbers; the

constants

are then

m

=

1

and

a

=

6

⁢

n

.

These numbers were first studied by Kevin Brown, who was searching for prime solutions to

2

n

-

1

+

n

. Helmut Zeisel replied that 1885 is such an

n

. Brown discovered that its

prime factors

fit the recurrrence

relation

with

m

=

2

and

a

=

3

. He called numbers fitting such a recurrence relation “Zeisel numbers” and the term has stuck, being taken up by the OEIS, MathWorld and Wikipedia. Zeisel himself has suggested the term “Brown-Zeisel number” but this has not caught on. There is a different

concept

of the Zeisel number used in chemistry.

Title

Zeisel number

Canonical name

ZeiselNumber

Date of creation

2013-03-22 17:44:03

Last modified on

2013-03-22 17:44:03

Owner

CompositeFan (12809)

Last modified by

CompositeFan (12809)

Numerical id

6

Author

CompositeFan (12809)

Entry type

Definition

Classification

msc 11A25

Defines

Brown-Zeisel number

Generated on Fri Feb 9 15:15:39 2018 by

LaTeXML
zero

zero

Zero

(or

null

or

nought

) is the

integer

between

-

1

and 1, usually represented as 0 (the glyph had a diagonal slash in early

computer

fonts). In the

complex plane

, zero is at the

intersection

of the line of numbers with no

imaginary part

and the line of numbers with no

real part

, and as such can be represented as

0

+

0

⁢

i

.

Zero is an

identity element

for

addition

, meaning that adding 0 to another number just gives that other number:

x

+

0

=

x

. But under

multiplication

, 0 is a fixed element:

0

⁢

x

=

0

. Also,

0

x

=

0

, but

division by zero

is not allowed for most applications. Whether

x

is

positive

or negative,

x

0

=

1

. But

0

0

is a whole other can of worms.

As a digit in a positional base, 0 indicates the absence of a particular power of the base in the

partition

representing a given number. For example, in the base 10

self-descriptive number

6210001000, the 0s indicate the absence of ones, tens,

hundreds

, ten thousands, hundred thousands, and millions in this particular

representation

of this number. For computers and their binary representation of numbers, a bit set to 0 is a bit that is off, having no electrical current at the moment.

Though not as late as for the

negative numbers

, the concept of zero met with some resistance at first. But by the 20th Century, 0 had become indispensable for all branches of mathematics. In elementary algebra textbooks, 0 is often the goal of solving a problem, e.g., the

quadratic equation

4

⁢

x

2

+

3

⁢

x

+

1

=

0

, in which the student is asked to find the value of

x

that makes the left-side of the

equation

equal to zero. Even Euler’s

identity

is sometimes stated in this way:

e

i

⁢

π

+

1

=

0

.

Given a

function

f

, the values

x

such that

f

⁢

(

x

)

=

0

are called the “zeroes” of that function and are often of special

interest

to mathematicians and amateurs alike; see: zero of a function (

http://planetmath.org/ZeroOfAFunction

). (For example, the zeroes of the

Riemann zeta function

).

For more on zero through the ages, see: history of zero.

Title

zero

Canonical

name

Zero

Date of creation

2013-03-22 18:04:09

Last modified on

2013-03-22 18:04:09

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

7

Author

Mravinci (12996)

Entry type

Definition

Classification

msc 11A25

Synonym

null

Synonym

nought

Related topic

IsomorphismSwappingZeroAndUnity

Generated on Fri Feb 9 15:15:40 2018 by

LaTeXML
σ function

σ

function

Given a

positive integer

n

, the sum of the

integers

0

<

d

≤

n

such that

d

|

n

is the value of the

sum of divisors function

for

n

, often symbolized by a Greek lowercase

σ

. Thus,

σ

⁢

(

n

)

=

∑

d

|

n

d

.

Sometimes this

function

is referred to as

σ

1

⁢

(

n

)

, highlighting its relation to the

divisor function

.

Given coprime integers

m

and

n

(that is,

gcd

⁡

(

m

,

n

)

=

1

) then

σ

⁢

(

m

⁢

n

)

=

σ

⁢

(

m

)

⁢

σ

⁢

(

n

)

, meaning that the sum of divisors function is a

multiplicative function

.

Title

σ

function

Canonical name

sigmaFunction

Date of creation

2013-03-22 16:07:12

Last modified on

2013-03-22 16:07:12

Owner

CompositeFan (12809)

Last modified by

CompositeFan (12809)

Numerical id

8

Author

CompositeFan (12809)

Entry type

Definition

Classification

msc 11A25

Synonym

divisor sigma

Synonym

sum of divisors function

Synonym

σ

1

function

Generated on Fri Feb 9 15:15:42 2018 by

LaTeXML
τ function

τ

function

The

τ

function

, also called the

divisor function

, takes a

positive integer

as its input and gives the number of

positive

divisors

of its input as its output. For example, since

1

,

2

, and

4

are all of the positive divisors of

4

, we have

τ

⁢

(

4

)

=

3

. As another example, since

1

,

2

,

5

, and

10

are all of the positive divisors of

10

, we have

τ

⁢

(

10

)

=

4

.

The

τ

function behaves according to the following two rules:

1. If

p

is a prime and

k

is a

nonnegative integer

, then

τ

⁢

(

p

k

)

=

k

+

1

.

2. If

gcd

⁡

(

a

,

b

)

=

1

, then

τ

⁢

(

a

⁢

b

)

=

τ

⁢

(

a

)

⁢

τ

⁢

(

b

)

.

Because these two rules hold for the

τ

function, it is a

multiplicative function

.

Note that these rules work for the previous two examples. Since

2

is prime, we have

τ

⁢

(

4

)

=

τ

⁢

(

2

2

)

=

2

+

1

=

3

. Since

2

and

5

are distinct primes, we have

τ

⁢

(

10

)

=

τ

⁢

(

2

⋅

5

)

=

τ

⁢

(

2

)

⁢

τ

⁢

(

5

)

=

(

1

+

1

)

⁢

(

1

+

1

)

=

4

.

If

n

is a positive integer, the number of

prime factors

(

http://planetmath.org/UFD

) of

x

n

-

1

over

ℚ

⁢

[

x

]

is

τ

⁢

(

n

)

. For example,

x

9

-

1

=

(

x

3

-

1

)

⁢

(

x

6

+

x

3

+

1

)

=

(

x

-

1

)

⁢

(

x

2

+

x

+

1

)

⁢

(

x

6

+

x

3

+

1

)

and

τ

⁢

(

9

)

=

3

.

The

τ

function is extremely useful for studying

cyclic rings

.

The

sequence

{

τ

⁢

(

n

)

}

appears in the OEIS as sequence

http://www.research.att.com/ njas/sequences/A000005

A000005.

Title

τ

function

Canonical name

tauFunction

Date of creation

2013-03-22 13:30:16

Last modified on

2013-03-22 13:30:16

Owner

Wkbj79 (1863)

Last modified by

Wkbj79 (1863)

Numerical id

21

Author

Wkbj79 (1863)

Entry type

Definition

Classification

msc 11A25

Synonym

divisor function

Related topic

Divisor

Related topic

DirichletHyperbolaMethod

Related topic

2omeganLeTaunLe2Omegan

Related topic

Divisibility

Related topic

ValuesOfNForWhichVarphintaun

Related topic

LambertSeries

Related topic

ParityOfTauFunction

Generated on Fri Feb 9 15:15:44 2018 by

LaTeXML
a prime occurs in the Euclid-Mullin sequence no more than once

a prime occurs in the Euclid-Mullin sequence no more than once

Theorem.

A prime

p

which occurs in the

Euclid-Mullin sequence

a

starting with 2 (or any variant made by changing the initial value to an

odd prime

) occurs only once.

Whether

a

1

=

2

or some odd prime, each succeeding term is the least

prime factor

of the product of the previous terms plus 1.

The proof is barely little more than a rehashing of Euclid’s proof that there are infinitely many primes.

Proof.

We begin by asserting that

p

does indeed occur twice in the Euclid-Mullin sequence (or some variant thereof), and that the second occurrence is at position

n

. Or, to put it algebraically, the first occurrence is at position

m

and there is an

n

>

m

such that

a

n

=

a

m

.

For our convenience, we assign

α

j

thus:

α

j

=

∏

i

=

1

j

-

1

a

i

.

Obviously

α

n

is

divisible

by each

a

i

for

i

<

n

, and that obviously includes

a

m

. Without yet concerning ourselves with

primality

, then it is obvious that

α

n

+

1

is not divisible by any of the previous

a

i

, and that also includes

a

m

. If

α

n

+

1

is indeed prime, then

a

n

=

α

+

1

and

a

n

>

a

i

, often spectacularly so, obviously contradicting our initial assertion. But if

α

n

+

1

is

composite

, its least prime factor can’t be any of the previous

a

i

, because they’re all factors of

α

n

, and we now invoke the proof that two consecutive

integers

are always

coprime

.
∎

When

α

n

+

1

is prime the proof is undoubtable; it is a prime greater than all the previous primes in the

sequence

. But if there is any doubt whatsoever when

α

n

+

1

is composite, it might perhaps be at least a tiny bit worthwhile to work out an example: I assert that

a

5

in the Euclid-Mullin sequence is a repeated term. The first four terms of the Euclid-Mullin sequence are 2, 3, 7, 43. Their product is 1806, which is obviously even, and it is also divisible by 3. It’s up to you whether you want to use a

divisibility test

for 7 or just perform the calculation to verify that 1806 is indeed divisible by 7. And 1806 is 43 times… 42. 1807 can’t be divisible by any of the same positive numbers 1806 is divisible by (other than of course 1). But it’s nowhere to be found on a list of prime numbers. It’s not divisible by 11 but it turns out to be divisible by 13. 13, though smaller than 43, is clearly not equal to either 2, 3 or 7. Therefore my initial assertion is incorrect.

Title

a prime occurs in the Euclid-Mullin sequence no more than once

Canonical name

APrimeOccursInTheEuclidMullinSequenceNoMoreThanOnce

Date of creation

2013-03-22 17:41:29

Last modified on

2013-03-22 17:41:29

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Theorem

Classification

msc 11A41

Generated on Fri Feb 9 15:15:46 2018 by

LaTeXML
Andrica’s conjecture

Andrica’s conjecture

Conjecture

(Dorin Andrica). Given the

n

th prime

p

n

, it is always the case that

1

>

p

n

+

1

-

p

n

.

This conjecture remains unproven as of 2007. The conjecture has been checked up to

n

=

10

5

by

computers

.

The largest known

difference of square

roots of consecutive primes happens for the small

n

=

4

, being approximately 0.67087347929081. The

difference

of the

square roots

of the primes

10

314

-

1929

and

10

314

+

2318

(which cap a

prime gap

of 4247 consecutive

composite numbers

discovered in 1992 by Baugh & O’Hara) is a very small number which is obviously much smaller than 1.

References

1

D. Baugh & F. O’Hara, “Large Prime Gaps”

J. Recr. Math.

24

(1992): 186 - 187.

Title

Andrica’s conjecture

Canonical

name

AndricasConjecture

Date of creation

2013-03-22 16:41:22

Last modified on

2013-03-22 16:41:22

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

8

Author

PrimeFan (13766)

Entry type

Conjecture

Classification

msc 11A41

Synonym

Andrica conjecture

Generated on Fri Feb 9 15:15:47 2018 by

LaTeXML
balanced prime

balanced prime

If for the given

n

th prime

p

n

the equality

p

n

=

1

3

⁢

∑

i

=

n

-

1

n

+

1

p

i

is true, then

p

n

is said to be a

balanced prime

. That is, the

arithmetic mean

of the given prime, the prime immediately below and the one immediately above, is equal to the middle prime. The first few are 5, 53, 157, 173, 211, 257, 263, 373, listed in A006562 of Sloane’s OEIS. As of 2006, the largest known balanced prime is

197418203

×

2

25000

-

1

, discovered by David Broadhurst and FranÃÂ§ois Morain using FastECPP and PrimeForm.

Title

balanced prime

Canonical

name

BalancedPrime

Date of creation

2013-03-22 16:36:50

Last modified on

2013-03-22 16:36:50

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 11A41

Related topic

StrongPrime

Related topic

WeakPrime

Generated on Fri Feb 9 15:15:49 2018 by

LaTeXML
Brocard’s conjecture

Brocard’s conjecture

(Henri Brocard) With the exception of 4 and 9, there are always at least four

prime numbers

between the square of a prime and the square of the next prime. To put it algebraically, given the

n

th prime

p

n

(with

n

>

1

), the inequality

(

π

⁢

(

p

n

+

1

2

)

-

π

⁢

(

p

n

2

)

)

>

3

is always true, where

π

⁢

(

x

)

is the

prime counting function

.

For example, between

2

2

and

3

2

there are only two primes: 5 and 7. But between

3

2

and

5

2

there are five primes: a

prime quadruplet

(11, 13, 17, 19) and 23.

This conjecture remains unproven as of 2007. Thanks to computers, brute force searches have shown that the conjecture holds true as high as

n

=

10

4

.

Title

Brocard’s conjecture

Canonical name

BrocardsConjecture

Date of creation

2013-03-22 16:40:53

Last modified on

2013-03-22 16:40:53

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

8

Author

PrimeFan (13766)

Entry type

Conjecture

Classification

msc 11A41

Synonym

Brocard conjecture

Related topic

LegendresConjecture

Generated on Fri Feb 9 15:15:54 2018 by

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Chebyshev functions

Chebyshev functions

There are two different

functions

which are collectively known as the

Chebyshev functions

:

ϑ

⁢

(

x

)

=

∑

p

≤

x

log

⁡

p

.

where the notation used indicates the

summation

over all

positive

primes

p

less than or equal to

x

, and

ψ

⁢

(

x

)

=

∑

p

≤

x

k

⁢

log

⁡

p

,

where the same summation notation is used and

k

denotes the unique

integer

such that

p

k

≤

x

but

p

k

+

1

>

x

. Heuristically, the first of these two functions the number of primes less than

x

and the second does the same, but weighting each prime in accordance with their logarithmic relationship to

x

.

Many innocuous results in number owe their proof to a relatively

analysis

of the asymptotics of one or both of these functions. For example, the fact that for any

n

, we have

∏

p

≤

n

p

<

4

n

is

equivalent

to the statement that

ϑ

⁢

(

x

)

<

x

⁢

log

⁡

4

.

A somewhat less innocuous result is that the

prime number theorem

(i.e., that

π

⁢

(

x

)

∼

x

log

⁡

x

) is equivalent to the statement that

ϑ

⁢

(

x

)

∼

x

, which in turn, is equivalent to the statement that

ψ

⁢

(

x

)

∼

x

.

References

1

Ireland, Kenneth and Rosen, Michael. A Classical

Introduction

to Modern

Number Theory

. Springer, 1998.

2

Nathanson, Melvyn B.

Elementary Methods

in Number Theory. Springer, 2000.

Title

Chebyshev functions

Canonical

name

ChebyshevFunctions

Date of creation

2013-03-22 13:50:15

Last modified on

2013-03-22 13:50:15

Owner

Mathprof (13753)

Last modified by

Mathprof (13753)

Numerical id

11

Author

Mathprof (13753)

Entry type

Definition

Classification

msc 11A41

Related topic

MangoldtSummatoryFunction

Generated on Fri Feb 9 15:15:56 2018 by

LaTeXML
composite number

composite number

A

composite number

is a

positive integer

which is not prime and not equal to 1. That is,

n

is composite if

n

=

a

⁢

b

, with

a

and

b

natural numbers both not equal to 1.

Examples.

•

1 is not composite (and also not prime), by

definition

.

•

2 is not composite, as it is prime.

•

15 is composite, since

15

=

3

⋅

5

.

•

93555 is composite, since

93555

=

3

5

⋅

5

⋅

7

⋅

11

.

•

52223 is not composite, since it is prime.

More generally, we can define compositeness any time there is an ambient notion of an

irreducible element

. In an

integral domain

, for example, an element is said to be

composite

if it neither zero, a unit, nor irreducible.

Title

composite number

Canonical

name

CompositeNumber

Date of creation

2013-03-22 12:39:37

Last modified on

2013-03-22 12:39:37

Owner

mathcam (2727)

Last modified by

mathcam (2727)

Numerical id

9

Author

mathcam (2727)

Entry type

Definition

Classification

msc 11A41

Synonym

composite

Generated on Fri Feb 9 15:15:58 2018 by

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Compositorial

Compositorial

The

compositorial

of a number n equals the product of

composite numbers

less than or equal to n. For example, the compositorial of 6 is 24 since the composite numbers less than or equal to 6 are 4 and 6 and 4 * 6 = 24. Similarly the distinct compositorial numbers are 1, 4, 24, 192, 1728, 17280, 207360 and so on (

Sequence

A036991 of OEIS).

The numbers whose compositorial minus 1 is a

prime number

are 1, 2, 3 , 4, 5, 8, 14, 20, 26 … (Sequence A140294 of OEIS). The numbers whose compositorial plus 1 is a prime number are 4, 5, 6, 7, 8, 16, 17, 21, 24 … (Sequence 140293 of OEIS).

Title

Compositorial

Canonical

name

Compositorial

Date of creation

2013-03-22 19:20:40

Last modified on

2013-03-22 19:20:40

Owner

Kausthub (26471)

Last modified by

Kausthub (26471)

Numerical id

4

Author

Kausthub (26471)

Entry type

Definition

Classification

msc 11A41

Generated on Fri Feb 9 15:15:59 2018 by

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