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

Author

Henry Bottomley, Apr 12 2001

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Magma

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

Mathematica

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

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.