A303756 Number of values of k, 1 <= k <= n, with A002322(k) = A002322(n), where A002322 is Carmichael lambda.

1, 2, 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 A002322.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A002322.

Cf. also A081373, A303755, A303758.

Programs

Mathematica

a[n_] := With[{c = CarmichaelLambda[n]}, Select[Range[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
v303756 = ordinal_transform(vector(up_to,n,A002322(n)));
A303756(n) = v303756[n];

Formula

Except for a(2) = 2, a(n) = A303758(n).