|
Search: id:A014197
|
|
|
| A014197 |
|
Number of numbers m with Euler phi(m) = n. |
|
+0
27
|
|
| 2, 3, 0, 4, 0, 4, 0, 5, 0, 2, 0, 6, 0, 0, 0, 6, 0, 4, 0, 5, 0, 2, 0, 10, 0, 0, 0, 2, 0, 2, 0, 7, 0, 0, 0, 8, 0, 0, 0, 9, 0, 4, 0, 3, 0, 2, 0, 11, 0, 0, 0, 2, 0, 2, 0, 3, 0, 2, 0, 9, 0, 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 17, 0, 0, 0, 0, 0, 2, 0, 10, 0, 2, 0, 6, 0, 0, 0, 6, 0, 0, 0, 3
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Carmichael conjectured that there are no 1's in this sequence.
Number of cyclotomic polynomials of degree n. - T. D. Noe (noe(AT)sspectra.com), Aug 15 2003
|
|
REFERENCES
|
R. K. Guy, Unsolved Problems in Number Theory, section B39.
J. Roberts, Lure of The Integers, entry 32, page 182.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n = 1..10000
K. Ford, [math/9907204] The number of solutions of phi(x)=m
Primefan, Totient Answers For The First 1000 Integers
Eric Weisstein's World of Mathematics, Totient Function
Eric Weisstein's World of Mathematics, Totient Valence Function
|
|
FORMULA
|
Dirichlet g.f.: sum(n>=1, a(n)*n^-s)=zeta(s)*prod(1+1/(p-1)^s-1/p^s) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 12 2003
lim n ->infinity (1/n)*sum(k=1, n, a(k))=zeta(2)*zeta(3)/zeta(6)=1.94359643682075920505707036... - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 12 2003
|
|
MAPLE
|
with(numtheory): A014197 := n-> nops(invphi(i));
|
|
CROSSREFS
|
Cf. A058277, A002202, A032446.
Cf. A070243 (partial sums).
For records see A131934, A097942.
Adjacent sequences: A014194 A014195 A014196 this_sequence A014198 A014199 A014200
Sequence in context: A137663 A161628 A122059 this_sequence A021438 A025638 A025639
|
|
KEYWORD
|
nonn,nice,easy
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
Additional comments from Jud McCranie (j.mccranie(AT)comcast.net), Oct 10 2000
|
|
|
Search completed in 0.002 seconds
|
