cp's OEIS Frontend

A244800 Number of moduli m such that (prime(n) mod m) is even, where 1 <= m < prime(n).

%I A244800 #16 Jun 13 2021 03:23:25
%S A244800 2,2,3,3,5,5,8,7,9,12,10,14,16,14,18,20,22,20,25,25,24,28,31,33,35,37,
%T A244800 35,41,39,39,44,45,51,49,56,52,54,55,61,62,66,62,68,68,73,69,72,76,83,
%U A244800 81,85,83,81,88,93,95,95,89,97,99,97,103,107,105,103,113
%N A244800 Number of moduli m such that (prime(n) mod m) is even, where 1 <= m < prime(n).
%C A244800 a(n) + A244799(n) = A000040(n) = prime(n).
%H A244800 Clark Kimberling, <a href="/A244800/b244800.txt">Table of n, a(n) for n = 1..1000</a>
%e A244800 In the following table, mh abbreviates mod(h) and p(n) = prime(n).
%e A244800 n . p(n) . m2 . m3 . m4 . m5 . m6 . m7 . m8 . m9 . m10 . m11 #odd #even
%e A244800 1 . 2 .... 0 .. 0 ........................................... 0 .. 2
%e A244800 2 . 3 .... 0 .. 1 .. 0 ...................................... 1 .. 2
%e A244800 3 . 5 .... 0 .. 1 .. 2 .. 1 .. 0 ............................ 2 .. 3
%e A244800 4 . 7 .... 0 .. 1 .. 1 .. 3 .. 2 .. 1 .. 0 .................. 4 .. 3,
%e A244800 so that A244800 = (2,2,3,3,...) and A244799 = (0,1,2,4,...).
%t A244800 z = 1000; f[n_, m_] := If[EvenQ[Mod[Prime[n], m]], 1, 0]
%t A244800 t = Table[f[n, m], {n, 1, z}, {m, 1, Prime[n]}];
%t A244800 Table[Count[t[[k]], 1], {k, 1, z}] (* A244800 *)
%Y A244800 Cf. A244799, A000040.
%K A244800 nonn,easy
%O A244800 1,1
%A A244800 _Clark Kimberling_, Jul 06 2014