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

1,4

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

Formula

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

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 *)

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; };
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];

Crossrefs

Cf. A002322.

Cf. also A303756, A303757.

Sequence in context: A132460 A238800 A067734 * A161904 A360678 A346697

Adjacent sequences: A303755 A303756 A303757 * A303759 A303760 A303761

Keyword

nonn

Author

Antti Karttunen, Apr 30 2018

Status

approved