A303758 a(1) = 1 and for n > 1, a(n) = number of values of k, 2 <= k <= n, with A002322(k) = A002322(n), where A002322 is Carmichael lambda.

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

Offset: 1

Author

Antti Karttunen, Apr 30 2018

Keywords

• nonn

Comments

Ordinal transform of f, where f(1) = 0 and f(n) = A002322(n) for n > 1.

Links

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

Crossrefs

Cf. A002322.

Cf. also A303756, A303757.

Programs

Mathematica

a[1] = 1; a[n_] := With[{c = CarmichaelLambda[n]}, Select[Range[2, n], c == CarmichaelLambda[#]&] // Length];
Array[a, 1000] (* Jean-François Alcover, Sep 19 2020 *)

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; };
A002322(n) = lcm(znstar(n)[2]); \\ From A002322
Aux303758(n) = if(1==n,0,A002322(n));
v303758 = ordinal_transform(vector(up_to,n,Aux303758(n)));
A303758(n) = v303758[n];

Formula

Except for a(2) = 1, a(n) = A303756(n).