Statements (54)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
integer sequence
|
| gptkbp:author |
gptkb:N._J._A._Sloane
|
| gptkbp:citation |
gptkb:A000203
gptkb:A001615 gptkb:A002322 gptkb:A005117 gptkb:A007770 gptkb:A008683 gptkb:A013929 A027375 A046970 A054525 A064216 A099788 A109606 A122111 |
| gptkbp:eighth_term |
4
|
| gptkbp:fifthBook |
4
|
| gptkbp:first_terms |
1
|
| gptkbp:form |
phi(n) = n * Product_{p|n} (1 - 1/p), where p runs over the distinct prime divisors of n
|
| gptkbp:fourthPlace |
2
|
| gptkbp:hasKeyword |
easy
nonn mult |
| https://www.w3.org/2000/01/rdf-schema#label |
A000010 (OEIS)
|
| gptkbp:mathematical_property |
Dirichlet inverse is the Möbius function
phi(n) is the number of elements of order n in a cyclic group of order n phi(n) counts generators of cyclic group of order n phi(n) is the number of irreducible polynomials of degree n over GF(2) average order is 6n/(pi^2) phi(n) is even for n > 2 phi(p) = p-1 for prime p sum_{d|n} phi(d) = n sum_{k=1}^{n} phi(k) ~ 3n^2/(pi^2) phi(n) is the degree of the splitting field of x^n-1 over Q phi(n) is the number of primitive n-th roots of unity |
| gptkbp:name |
gptkb:Euler_totient_function
|
| gptkbp:ninth_term |
6
|
| gptkbp:OEIS |
A000010
|
| gptkbp:related_sequence |
gptkb:A001221
gptkb:A007434 |
| gptkbp:relatedConcept |
gptkb:Euler's_totient_function
|
| gptkbp:sequence |
arithmetic function
multiplicative function number-theoretic function |
| gptkbp:sequence_definition |
Number of positive integers <= n that are coprime to n
|
| gptkbp:seventhBook |
6
|
| gptkbp:sixthBook |
2
|
| gptkbp:tenth_term |
4
|
| gptkbp:thirdPlace |
2
|
| gptkbp:bfsParent |
gptkb:Euler's_totient_function
gptkb:Euler's_totient_function_φ(n) gptkb:Euler's_function |
| gptkbp:bfsLayer |
6
|