A303777 Ordinal transform of A081373; ordinal transform of {the ordinal transform of A000010}.

1, 1, 2, 2, 3, 1, 4, 3, 4, 2, 5, 1, 6, 3, 7, 5, 8, 2, 9, 4, 6, 7, 10, 3, 11, 5, 8, 4, 12, 1, 13, 9, 10, 6, 14, 2, 15, 7, 11, 5, 16, 1, 17, 8, 9, 12, 18, 3, 13, 6, 19, 7, 20, 8, 14, 4, 15, 16, 21, 2, 22, 17, 10, 18, 23, 5, 24, 11, 25, 3, 26, 1, 27, 9, 12, 6, 19, 1, 28, 10, 29, 11, 30, 1, 31, 13, 32, 7, 33, 1, 20, 21, 14, 22, 15, 8

Offset: 1

Author

Antti Karttunen, Apr 30 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000010, A081373, A081375 (positions of ones), A210719 (positions of records), A286610.

Programs

Maple

b:= proc() 0 end: g:= proc() 0 end:
h:= proc(n) option remember; local t;
      t:= numtheory[phi](n); b(t):= b(t)+1
    end:
a:= proc(n) option remember; local t;
      t:= h(n); g(t):= g(t)+1
    end:
seq(a(n), n=1..120);  # Alois P. Heinz, Apr 30 2018

Mathematica

b[] = 0; g[] = 0;
h[n_] := h[n] = With[{t = EulerPhi[n]}, b[t] = b[t]+1];
a[n_] := a[n] = With[{t = h[n]}, g[t] = g[t]+1];
Array[a, 120] (* Jean-François Alcover, Dec 19 2021, after Alois P. Heinz *)

PARI

up_to = 65537;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
v081373 = ordinal_transform(vector(up_to,n,eulerphi(n)));
A081373(n) = v081373[n];
v303777 = ordinal_transform(vector(up_to,n,A081373(n)));
A303777(n) = v303777[n];