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A286477 Ordinal transform of A032742, starting from its first term a(1) = 1.

%I A286477 #11 Dec 24 2021 08:10:47
%S A286477 1,2,3,1,4,1,5,1,2,1,6,1,7,1,2,1,8,1,9,1,2,1,10,1,3,1,2,1,11,1,12,1,2,
%T A286477 1,3,1,13,1,2,1,14,1,15,1,2,1,16,1,4,1,2,1,17,1,3,1,2,1,18,1,19,1,2,1,
%U A286477 3,1,20,1,2,1,21,1,22,1,2,1,4,1,23,1,2,1,24,1,3,1,2,1,25,1,4,1,2,1,3,1,26,1,2,1,27,1,28,1,2,1,29,1,30,1,2,1,31
%N A286477 Ordinal transform of A032742, starting from its first term a(1) = 1.
%C A286477 If we instead apply the ordinal transform to A032742 starting from its second term a(2) = 1, the result seems to be a shifted version of A055396.
%H A286477 Antti Karttunen, <a href="/A286477/b286477.txt">Table of n, a(n) for n = 1..10000</a>
%t A286477 Function[{s, t}, ReplacePart[t, Flatten@ Map[MapIndexed[#1 -> First@ #2 &, #] &, Values@ s]]] @@ {PositionIndex@ #, ConstantArray[0, Length@ #]} & Table[n/FactorInteger[n][[1, 1]], {n, 113}] (* _Michael De Vlieger_, May 12 2017, Version 10 *)
%t A286477 b[_] = 0;
%t A286477 a[n_] := a[n] = With[{t = If[n == 1, 1, Divisors[n][[-2]]]}, b[t] = b[t]+1];
%t A286477 Array[a, 1000] (* _Jean-François Alcover_, Dec 24 2021 *)
%Y A286477 Cf. A032742, A055396.
%K A286477 nonn
%O A286477 1,2
%A A286477 _Antti Karttunen_, May 12 2017