A285014 Number of integers b with 1 < b < c such that b^(c-1) == 1 (modulo c), where c is the n-th composite number.

0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 3, 0, 1, 2, 0, 0, 3, 0, 3, 0, 0, 3, 0, 0, 0, 7, 0, 0, 5, 0, 3, 2, 0, 3, 0, 3, 0, 0, 0, 3, 0, 15, 4, 0, 3, 2, 0, 0, 3, 2, 3, 0, 0, 1, 0, 0, 15, 0, 3, 0, 0, 35, 0, 3, 0, 3, 0, 0, 3, 0, 0, 0, 15, 0, 0, 0, 3, 2, 0, 3, 0, 7

Offset

1,8

Comments

a(n) > 1 iff c is a term of A039769, i.e., iff A268310(n) > 0.

Links

Table of n, a(n) for n=1..86.

Example

For n = 8: A002808(8) = 15 and b^(15-1) == 1 (modulo 15) for three values of b with 1 < b < c, namely 4, 11, 14, so a(8) = 3.

Mathematica

DeleteCases[Table[If[CompositeQ@ n, Count[Range[2, n - 1], b_ /; Mod[b^(n - 1), n] == 1], -1], {n, 117}], -1] (* Michael De Vlieger, May 09 2017 *)

Prog

(PARI) forcomposite(c=1, 200, my(i=0); for(b=2, c-1, if(Mod(b, c)^(c-1)==1, i++)); print1(i, ", "))

Crossrefs

Cf. A002808, A039769, A268310.

Sequence in context: A308347 A090225 A206705 * A219551 A200221 A158678

Adjacent sequences: A285011 A285012 A285013 * A285015 A285016 A285017

Keyword

nonn

Author

Felix Fröhlich, May 09 2017

Status

approved