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A289152 Ordinal transform of A003434. 1

%I

%S 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,

%T 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,

%U 23,6,24,7,25,26,8,9,27,10,11,12,28,13,29,14,30,15

%N Ordinal transform of A003434.

%C 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).

%C This sequence has graphical similarities with A286343.

%H Rémy Sigrist, <a href="/A289152/b289152.txt">Table of n, a(n) for n = 1..10000</a>

%e The first terms are:

%e n A003434(n) a(n)

%e -- ---------- ----

%e 1 0 1

%e 2 1 1

%e 3 2 1

%e 4 2 2

%e 5 3 1

%e 6 2 3

%e 7 3 2

%e 8 3 3

%e 9 3 4

%e 10 3 5

%e 11 4 1

%e 12 3 6

%e 13 4 2

%e 14 3 7

%e 15 4 3

%e 16 4 4

%e 17 5 1

%e 18 3 8

%e 19 4 5

%e 20 4 6

%t 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 *)

%o (PARI) A003434(n) = for (k=0, oo, if (n==1, return (k), n=eulerphi(n)))

%o o = vector(10); for (n=1, 100, v=A003434(n); o[1+v]++; print1(o[1+v] ", "))

%Y Cf. A002260, A003434, A286343.

%K nonn,look

%O 1,4

%A _Rémy Sigrist_, Jun 26 2017

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Last modified January 18 14:07 EST 2021. Contains 340254 sequences. (Running on oeis4.)