A061498 Number of distinct terms in the first difference sequence of reduced residue system[=dRRS] for n.

0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 3, 2, 1, 2, 2, 2, 2, 2, 1, 3, 1, 1, 3, 2, 3, 2, 1, 2, 3, 2, 1, 3, 1, 2, 3, 2, 1, 2, 2, 2, 3, 2, 1, 2, 3, 2, 3, 2, 1, 3, 1, 2, 3, 1, 3, 3, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 3, 1, 2, 2, 2, 1, 3, 3, 2, 3, 2, 1, 3, 3, 2, 3, 2, 3, 2, 1, 2, 3, 2, 1, 3, 1, 2, 5

Offset: 1

Author

Labos Elemer, Jun 12 2001

Keywords

• nonn

Examples

			For n=24, RRS={1, 5, 7, 11, 13, 17, 19, 23}, dRRS={4, 2, 4, 2, 4, 2, 4};
for n=32, dRRS={2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2};
for n=31, dRRS={1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...};
for n=34, RRS={1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 23, 25, 27, 29, 31, 33}, dRRS={2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2};
so a(24)=2, a(32)=1, a(31)=1, a(34)=2.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A076362.

Programs

Mathematica

Table[Length@ Union@ Differences@ Select[Range@ n, CoprimeQ[#, n] &], {n, 105}] (* Michael De Vlieger, Jul 15 2017 *)

PARI

a(n) = {my(va = select(x->(gcd(n, x)==1), [1..n])); vd = vector(#va-1, k, va[k+1] - va[k]); #Set(vd);} \\ Michel Marcus, Jul 08 2018