A334122 - OEIS

%I #54 Apr 21 2020 11:20:06

%S 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,

%T 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,

%U 45,39,33,27,20,13,5,60,53,46,39,32,24,16,8,0,63,55

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

%H Robert Israel, <a href="/A334122/b334122.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%p b:= proc(n) b(n):= `if`(n<2, 0, b(n-1)+`if`(isprime(n), n, 0)) end:

%p a:= n-> irem(b(n), n):

%p seq(a(n), n=1..80);  # _Alois P. Heinz_, Apr 15 2020

%t Mod[Accumulate[(# * Boole @ PrimeQ[#]) & /@ (r = Range[100])], r] (* _Amiram Eldar_, Apr 15 2020 *)

%o (Python) return (sum(i for i in range(n+1) if is_prime(i)) % n)

%o (PARI) a(n) = my(np=primepi(n)); vecsum(primes(np)) % n; \\ _Michel Marcus_, Apr 16 2020

%Y Cf. A000720, A034387, A090396.

%K nonn,easy,look

%O 1,3

%A _Christoph Schreier_, Apr 15 2020