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

Author

Rémy Sigrist, Jun 26 2017

Keywords

• nonn
• look

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.

Examples

			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
		

Links

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

Crossrefs

Cf. A002260, A003434, A286343.

Programs

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 *)

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] ", "))