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

1,9

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A076362.

Sequence in context: A024317 A024880 A029424 * A106029 A260311 A188431

Adjacent sequences: A061495 A061496 A061497 * A061499 A061500 A061501

Keyword

nonn

Author

Labos Elemer, Jun 12 2001

Status

approved