|
|
A092878
|
|
Number of initial odd numbers in class n of the iterated phi function.
|
|
3
|
|
|
1, 1, 2, 3, 5, 7, 13, 16, 24, 33, 47, 60, 94, 122, 155, 187, 266, 354, 409, 550, 734, 955, 1186, 1472, 1864, 2404, 3026, 3712, 4675, 5939, 7260, 8826, 10970, 13529, 16572, 20104, 24943, 30391, 36790, 44416, 53925, 65216, 78658, 94300, 114196, 136821
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Class n, for n>0, contains all numbers k such that n iterations of the Euler phi function applied to k yields 2; class 0 contains only the numbers 1 and 2. There is a conjecture that the smallest number in class n is always odd. This increasing sequence supports that conjecture. As shown by Shapiro, all the initial odd numbers in class n>0 are between 2^n and 2^(n+1).
|
|
REFERENCES
|
R. K. Guy, Unsolved Problems in Number Theory, 2nd Ed., New York, Springer-Verlag, 1994, B41.
|
|
LINKS
|
|
|
EXAMPLE
|
a(2) = 2 because the sequence of eight numbers 5,7,8,9,10,12,14,18 (which all take exactly 2 iterations of the phi function to produce 2) begins with 2 odd numbers.
|
|
MATHEMATICA
|
nMax=23; nn=2^nMax; c=Table[0, {nn}]; Do[c[[n]]=1+c[[EulerPhi[n]]], {n, 2, nn}]; Table[Length[Select[Flatten[Position[c, n]], #<=2^n && OddQ[ # ]&]], {n, 0, nMax}]
|
|
CROSSREFS
|
Cf. A003434 (iterations of phi(n) needed to reach 1).
Cf. A058811 (number of numbers in class n).
Cf. A135833 (number of Section I primes).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
T. D. Noe, Mar 10 2004, Nov 30 2007, Nov 18 2008
|
|
STATUS
|
approved
|
|
|
|