A340541 Primes p such that the product of (p mod q) for primes q < p is a multiple of the sum of (p mod q) for primes q < p.

3, 11, 17, 31, 59, 67, 73, 101, 103, 173, 179, 193, 199, 211, 223, 349, 401, 463, 491, 499, 557, 563, 569, 571, 577, 587, 607, 613, 619, 631, 673, 709, 751, 757, 769, 797, 809, 857, 859, 877, 911, 919, 929, 967, 1009, 1033, 1039, 1049, 1151, 1153, 1193, 1201, 1237, 1249, 1259, 1289, 1297, 1303

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 11 2021

Keywords

• nonn

Comments

Primes prime(n) such that A102647(n) is divisible by A033955(n).

Examples

			a(3) = 17 is a term since (17 mod q) for primes q=2,3,5,7,11,13 are 1,2,2,3,6,4, and 1*2*2*3*6*4 = 288 is divisible by 1+2+2+3+6+4 = 18.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A033955, A102647.

Programs

Maple

P:= [seq(ithprime(i),i=1..1000)]:
filter:= proc(n) local L,k;
  L:= [seq(P[n] mod P[k],k=1..n-1)];
  convert(L,`*`) mod convert(L,`+`) = 0
end proc:
S:=select(filter, [$2..1000]):
map(t -> P[t], S);

PARI

isok(p) = {if (isprime(p) && (p>2), my(s=0, t=1); forprime(q=2, p-1, my(x= p%q); s += x; t *= x;); !(t % s););} \\ Michel Marcus, Jan 11 2021