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A268372

Number of distinct primes (n mod k) for k=1..floor(n/2).

0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 1, 1, 1, 1, 3, 2, 2, 1, 2, 1, 4, 2, 3, 2, 4, 2, 4, 2, 3, 2, 3, 2, 5, 2, 5, 3, 4, 3, 6, 2, 5, 2, 5, 2, 6, 2, 5, 3, 6, 3, 7, 3, 6, 3, 7, 4, 8, 3, 7, 4, 7, 3, 8, 2, 8, 4, 7, 4, 9, 3, 8, 4, 8, 4, 9, 2, 9, 5, 8, 5, 9, 3, 8, 4

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OFFSET

1,11

LINKS

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

EXAMPLE

For k=1..15, the numbers (31 mod k) are 0, 1, 1, 3, 1, 1, 3, 7, 4, 1, 9, 7, 5, 3, 1; the primes are 3,3,7,7,5,3, so that a(31) = 3.

MATHEMATICA

t[n_] := Table[Mod[n, k], {k, 1, Floor[n/2]}]

p[n_] := DeleteDuplicates[Select[t[n], PrimeQ[#] &]]

Table[Length[p[n]], {n, 1, 200}]

PROG