A289152 Ordinal transform of A003434.

1, 1, 1, 2, 1, 3, 2, 3, 4, 5, 1, 6, 2, 7, 3, 4, 1, 8, 5, 6, 7, 8, 2, 9, 3, 10, 11, 12, 4, 13, 5, 6, 7, 8, 9, 14, 10, 15, 11, 12, 1, 16, 13, 14, 15, 16, 2, 17, 18, 19, 3, 20, 4, 17, 5, 21, 22, 23, 6, 24, 7, 25, 26, 8, 9, 27, 10, 11, 12, 28, 13, 29, 14, 30, 15

Offset

1,4

Comments

The ordinal transform mentioned is the one described in A002260: the ordinal transform of a sequence b(n) is the sequence t(n) = number of values in b(1),...,b(n) which are equal to b(n).

This sequence has graphical similarities with A286343.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Example

The first terms are:
    n    A003434(n)      a(n)
   --    ----------      ----
    1           0          1
    2           1          1
    3           2          1
    4           2          2
    5           3          1
    6           2          3
    7           3          2
    8           3          3
    9           3          4
   10           3          5
   11           4          1
   12           3          6
   13           4          2
   14           3          7
   15           4          3
   16           4          4
   17           5          1
   18           3          8
   19           4          5
   20           4          6

Mathematica

With[{nn = 75}, Function[s, Table[Count[#, Last@ #] &@ Take[s, n], {n, nn}]]@ Table[Length@ NestWhileList[EulerPhi, n, # != 1 &] - 1, {n, nn}]] (* Michael De Vlieger, Jun 27 2017 *)

Prog

(PARI) A003434(n) = for (k=0, oo, if (n==1, return (k), n=eulerphi(n)))
o = vector(10); for (n=1, 100, v=A003434(n); o[1+v]++; print1(o[1+v] ", "))

Crossrefs

Cf. A002260, A003434, A286343.

Sequence in context: A029163 A196191 A137661 * A363708 A285779 A319320

Adjacent sequences: A289149 A289150 A289151 * A289153 A289154 A289155

Keyword

nonn,look

Author

Rémy Sigrist, Jun 26 2017

Status

approved