A061008 a(n) = Sum_{j=1..n} (-(n-1)! mod n).

0, 1, 2, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 23, 23, 23

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Formula

a(n) = a(n-1) + A061007(n) = A061009(n) + 2. For n > 3, a(n) = pi(n) + 2 where pi(n) = A000720(n) is the number of primes less than or equal to n.

Example

a(6) = 5 since (-1 mod 1) + (-1 mod 2) + (-2 mod 3) + (-6 mod 4) + (-24 mod 5) + (-120 mod 6) = 0 + 1 + 1 + 2 + 1 + 0 = 5.

Mathematica

Join[{0, 1, 2}, a[n_]:= 2 + PrimePi[n]; Table[a[n], {n, 4, 100}]] (* Vincenzo Librandi, Aug 11 2017 *)

Prog

(Magma) [0, 1, 2] cat [ 2+#PrimesUpTo(n): n in [4..200] ]; // Vincenzo Librandi, Aug 11 2017

Crossrefs

Cf. A000040, A000142, A061006, A061007, A061009.

Sequence in context: A227401 A131813 A083038 * A256720 A091988 A023824

Adjacent sequences: A061005 A061006 A061007 * A061009 A061010 A061011

Keyword

nonn

Author

Henry Bottomley, Apr 12 2001

Status

approved