A266714 Number of k <= n such that (n mod k) is prime.

0, 0, 0, 0, 1, 1, 2, 3, 2, 3, 5, 4, 4, 6, 6, 5, 8, 7, 7, 7, 7, 7, 13, 7, 8, 11, 13, 8, 13, 10, 12, 12, 13, 10, 17, 9, 15, 16, 17, 11, 18, 14, 19, 14, 18, 12, 26, 13, 16, 19, 21, 15, 24, 14, 22, 16, 22, 18, 29, 13, 23, 22, 28, 14, 28, 18, 29, 22, 24, 18, 32

Offset

1,7

Links

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

Example

(11 mod k) gives 0,1,2,3,1,5,4,3,2,1,0, with primes 2,3,5,3,2, so a(11) = 5.

Mathematica

t[n_] := Table[Mod[n, k], {k, 1, n}]
p[n_] := Select[t[n], PrimeQ[#] &]
Table[Length[p[n]], {n, 1, 200}]

Prog

(PARI) a(n) = sum(k=2, n, isprime(n % k)); \\ Michel Marcus, Feb 04 2016

Crossrefs

Cf. A266715, A268372.

Sequence in context: A110976 A318271 A236483 * A151570 A341520 A059036

Adjacent sequences: A266711 A266712 A266713 * A266715 A266716 A266717

Keyword

nonn,easy

Author

Clark Kimberling, Feb 03 2016

Status

approved