|
|
A058277
|
|
Number of values of k such that phi(k) = n, where n runs through the values (A002202) taken by phi.
|
|
23
|
|
|
2, 3, 4, 4, 5, 2, 6, 6, 4, 5, 2, 10, 2, 2, 7, 8, 9, 4, 3, 2, 11, 2, 2, 3, 2, 9, 8, 2, 2, 17, 2, 10, 2, 6, 6, 3, 17, 4, 2, 3, 2, 9, 2, 6, 3, 17, 2, 9, 2, 7, 2, 2, 3, 21, 2, 2, 7, 12, 4, 3, 2, 12, 2, 8, 2, 10, 4, 2, 21, 2, 2, 8, 3, 4, 2, 3, 19, 5, 2, 8, 2, 2, 6, 2, 31, 2, 9, 10
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Carmichael (1922) conjectured that the number 1 never appears in this sequence. Sierpiński conjectured and Ford (1998) proved that all integers greater than 1 occur in the sequence. Erdős (1958) proved that if s >= 1 appears in the sequence then it appears infinitely often. - Nick Hobson, Nov 04 2006
|
|
REFERENCES
|
E. Lucas, Théorie des Nombres, Blanchard 1958.
|
|
LINKS
|
|
|
MATHEMATICA
|
max = 300; inversePhi[_?OddQ] = {}; inversePhi[1] = {1, 2}; inversePhi[m_] := Module[{p, nmax, n, nn}, p = Select[Divisors[m] + 1, PrimeQ]; nmax = m * Times @@ (p/(p-1)); n = m; nn = Reap[While[n <= nmax, If[EulerPhi[n] == m, Sow[n]]; n++]] // Last; If[nn == {}, {}, First[nn] ] ]; Reap[For[n = 1, n <= max, n = If[n == 1, 2, n+2], nn = inversePhi[n] ; If[nn != {} , Sow[nn // Length] ] ] ] // Last // First (* Jean-François Alcover, Nov 21 2013 *)
|
|
PROG
|
(Haskell)
import Data.List (group)
a058277 n = a058277_list !! (n-1)
a058277_list = map length $ group a007614_list
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Claude Lenormand (claude.lenormand(AT)free.fr), Jan 05 2001
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|