A331182 Number of values of k, 1 <= k <= n, with A083254(k) = A083254(n), where A083254(n) = 2*phi(n) - n.

1, 1, 2, 2, 1, 1, 1, 3, 2, 2, 1, 1, 1, 3, 3, 4, 1, 1, 1, 2, 3, 4, 1, 1, 2, 5, 2, 3, 1, 1, 1, 5, 1, 6, 1, 1, 1, 7, 3, 2, 1, 1, 1, 4, 4, 8, 1, 1, 2, 1, 2, 5, 1, 2, 1, 3, 3, 9, 1, 1, 1, 10, 4, 6, 1, 1, 1, 6, 1, 1, 1, 1, 1, 11, 2, 7, 1, 1, 1, 2, 2, 12, 1, 1, 2, 13, 2, 4, 1, 1, 1, 8, 3, 14, 1, 1, 1, 2, 2, 1, 1, 1, 1, 5, 1

Offset: 1

Author

Antti Karttunen, Jan 11 2020

Keywords

• nonn

Comments

Ordinal transform of A083254.

Links

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

Crossrefs

Cf. A000010, A083254.

Cf. also A081373, A331175, A331181.

Programs

Mathematica

Module[{b}, b[_] = 0;
a[n_] := With[{t = 2 EulerPhi[n] - n}, b[t] = b[t] + 1]];
Array[a, 105] (* Jean-François Alcover, Jan 12 2022 *)

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; };
A083254(n) = (2*eulerphi(n)-n);
v331182 = ordinal_transform(vector(up_to,n,A083254(n)));
A331182(n) = v331182[n];