A334122 a(n) is the sum of all primes <= n, mod n.

0, 0, 2, 1, 0, 4, 3, 1, 8, 7, 6, 4, 2, 13, 11, 9, 7, 4, 1, 17, 14, 11, 8, 4, 0, 22, 19, 16, 13, 9, 5, 0, 28, 24, 20, 16, 12, 7, 2, 37, 33, 28, 23, 17, 11, 5, 46, 40, 34, 28, 22, 16, 10, 3, 51, 45, 39, 33, 27, 20, 13, 5, 60, 53, 46, 39, 32, 24, 16, 8, 0, 63, 55

Offset: 1

Author

Christoph Schreier, Apr 15 2020

Keywords

• nonn
• easy
• look

Examples

			a(7) = (2+3+5+7) mod 7 = 17 mod 7 = 3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000720, A034387, A090396.

Programs

Maple

b:= proc(n) b(n):= `if`(n<2, 0, b(n-1)+`if`(isprime(n), n, 0)) end:
a:= n-> irem(b(n), n):
seq(a(n), n=1..80);  # Alois P. Heinz, Apr 15 2020

Mathematica

Mod[Accumulate[(# * Boole @ PrimeQ[#]) & /@ (r = Range[100])], r] (* Amiram Eldar, Apr 15 2020 *)

PARI

a(n) = my(np=primepi(n)); vecsum(primes(np)) % n; \\ Michel Marcus, Apr 16 2020

Python

from sympy import primerange
a = lambda n: sum(primerange(n + 1)) % n # David Radcliffe, May 10 2025

Formula

a(n) = A034387(n) mod n.