A244799 Number of moduli m such that (prime(n) mod m) is odd, where 1 <= m < prime(n).

0, 1, 2, 4, 6, 8, 9, 12, 14, 17, 21, 23, 25, 29, 29, 33, 37, 41, 42, 46, 49, 51, 52, 56, 62, 64, 68, 66, 70, 74, 83, 86, 86, 90, 93, 99, 103, 108, 106, 111, 113, 119, 123, 125, 124, 130, 139, 147, 144, 148, 148, 156, 160, 163, 164, 168, 174, 182, 180, 182

Offset

1,3

Comments

a(n) + A244800(n) = A000040(n) = prime(n).

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Example

In the following table, mh abbreviates mod(h) and p(n) = prime(n).
n . p(n) . m2 . m3 . m4 . m5 . m6 . m7 . m8 . m9 . m10 . m11 #odd #even
1 . 2 .... 0 .. 0 ........................................... 0 .. 2
2 . 3 .... 0 .. 1 .. 0 ...................................... 1 .. 2
3 . 5 .... 0 .. 1 .. 2 .. 1 .. 0 ............................ 2 .. 3
4 . 7 .... 0 .. 1 .. 1 .. 3 .. 2 .. 1 .. 0 .................. 4 .. 3,
so that A244799 = (0,1,2,4,...) and A244800 = (2,2,3,3,...).

Mathematica

z = 1000; f[n_, m_] := If[OddQ[Mod[Prime[n], m]], 1, 0]
t = Table[f[n, m], {n, 1, z}, {m, 1, Prime[n]}];
Table[Count[t[[k]], 1], {k, 1, z}] (* A244799 *)
Table[With[{p=Prime[n]}, Count[Mod[p, Range[p-1]], _?OddQ]], {n, 60}] (* Harvey P. Dale, Jul 24 2022 *)

Crossrefs

Cf. A244800, A000040.

Sequence in context: A331873 A331936 A364123 * A347262 A367224 A316350

Adjacent sequences: A244796 A244797 A244798 * A244800 A244801 A244802

Keyword

nonn,easy

Author

Clark Kimberling, Jul 06 2014

Status

approved