A319695 Number of distinct values obtained when Euler phi (A000010) is applied to proper divisors of n.

0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 3, 3, 1, 3, 1, 3, 3, 2, 1, 3, 2, 2, 3, 3, 1, 4, 1, 4, 3, 2, 3, 4, 1, 2, 3, 4, 1, 4, 1, 3, 5, 2, 1, 4, 2, 3, 3, 3, 1, 4, 3, 5, 3, 2, 1, 4, 1, 2, 4, 5, 3, 4, 1, 3, 3, 4, 1, 6, 1, 2, 5, 3, 3, 4, 1, 5, 4, 2, 1, 5, 3, 2, 3, 5, 1, 6, 3, 3, 3, 2, 3, 5, 1, 3, 5, 5, 1, 4, 1, 5, 7

Offset

1,6

Links

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

Example

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

Prog

(PARI) A319695(n) = { my(m=Map(), s, k=0); fordiv(n, d, if((d<n)&&!mapisdefined(m, s=eulerphi(d)), mapput(m, s, s); k++)); (k); };

Crossrefs

Cf. A000010, A319696.

Cf. also A304793, A305611, A316555, A316556, A319685 for similarly constructed sequences.

Sequence in context: A105220 A083654 A164878 * A029428 A167866 A101422

Adjacent sequences: A319692 A319693 A319694 * A319696 A319697 A319698

Keyword

nonn

Author

Antti Karttunen, Oct 02 2018

Status

approved