A319696 Number of distinct values obtained when Euler phi (A000010) is applied to the divisors of n.

1, 1, 2, 2, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 4, 4, 2, 3, 2, 4, 4, 2, 2, 4, 3, 2, 4, 4, 2, 4, 2, 5, 4, 2, 4, 5, 2, 2, 4, 5, 2, 4, 2, 4, 6, 2, 2, 5, 3, 3, 4, 4, 2, 4, 4, 6, 4, 2, 2, 5, 2, 2, 5, 6, 4, 4, 2, 4, 4, 4, 2, 7, 2, 2, 6, 4, 4, 4, 2, 6, 5, 2, 2, 6, 4, 2, 4, 6, 2, 6, 4, 4, 4, 2, 4, 6, 2, 3, 6, 6, 2, 4, 2, 6, 8

Offset

1,3

Links

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

Formula

a(n) = A319695(n) + [n (mod 4) != 2], where [ ] is the Iverson bracket, resulting 0 when n = 2 mod 4, and 1 otherwise.

a(n) = A000005(n) if and only if n is in A326835. - Amiram Eldar, Nov 15 2025

Example

For n = 6, it has four divisors: 1, 2, 3 and 6, and applying A000010 to these gives 1, 1, 2, 2, with just two distinct values, thus a(6) = 2.

Mathematica

a[n_] := CountDistinct[EulerPhi[Divisors[n]]]; Array[a, 100] (* Amiram Eldar, Nov 15 2025 *)

Prog

(PARI) A319696(n) = { my(m=Map(), s, k=0); fordiv(n, d, if(!mapisdefined(m, s=eulerphi(d)), mapput(m, s, s); k++)); (k); };

Crossrefs

Cf. A000010, A000005, A319695, A326835.

Cf. also A184395, A319686.

Sequence in context: A349949 A196067 A251141 * A320111 A234287 A380378

Adjacent sequences: A319693 A319694 A319695 * A319697 A319698 A319699

Keyword

nonn

Author

Antti Karttunen, Oct 02 2018

Status

approved