A066913 (sum of primes < n that do not divide n) (mod n).

0, 0, 2, 3, 0, 5, 3, 7, 5, 0, 6, 11, 2, 4, 3, 7, 7, 17, 1, 10, 4, 20, 8, 23, 20, 7, 16, 7, 13, 29, 5, 30, 14, 5, 8, 11, 12, 24, 25, 30, 33, 16, 23, 4, 3, 26, 46, 35, 27, 21, 2, 1, 10, 52, 35, 36, 17, 2, 27, 10, 13, 34, 50, 51, 28, 23, 32, 5, 59, 64, 0, 58, 55, 7, 29, 7, 1, 70, 1

Offset: 1

Author

Leroy Quet, Jan 22 2002

Keywords

• nonn

Examples

			a(8) = (3 + 5 + 7) (mod 8) = 7 because 3, 5 and 7 are the primes < 8 that do not divide 8.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A066911, A071089.

Programs

Mathematica

Table[Mod[Total[Select[Prime[Range[PrimePi[n]]],Mod[n,#]!=0&]],n],{n,80}] (* Harvey P. Dale, Aug 06 2019 *)

PARI

a(n) = sum(i=1, n-1, if (isprime(i) && (n%i), i)) % n; \\ Michel Marcus, May 20 2014

Formula

a(n) = A066911(n) modulo n. - Michel Marcus, May 20 2014

a(prime(n)) = A071089(n). - Michel Marcus, May 20 2014