A303753 Ordinal transform of cototient (A051953).

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

Offset

1,3

Comments

Number of values of k, 1 <= k <= n, with A051953(k) = A051953(n).

Links

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

Formula

For all n >= 1, a(A000040(n)) = n.

Maple

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

Mathematica

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

Prog

(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; };
A051953(n) = (n - eulerphi(n));
v303753 = ordinal_transform(vector(up_to, n, A051953(n)));
A303753(n) = v303753[n];

Crossrefs

Cf. A051953, A065385 (gives a subset of the positions of ones).

Cf. also A081373, A303754.

Sequence in context: A361441 A340088 A087114 * A088242 A228814 A299483

Adjacent sequences: A303750 A303751 A303752 * A303754 A303755 A303756

Keyword

nonn

Author

Antti Karttunen, Apr 30 2018

Status

approved