A340541 - OEIS

%I #13 Jan 12 2021 15:36:05

%S 3,11,17,31,59,67,73,101,103,173,179,193,199,211,223,349,401,463,491,

%T 499,557,563,569,571,577,587,607,613,619,631,673,709,751,757,769,797,

%U 809,857,859,877,911,919,929,967,1009,1033,1039,1049,1151,1153,1193,1201,1237,1249,1259,1289,1297,1303

%N 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.

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

%H Robert Israel, <a href="/A340541/b340541.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

%p P:= [seq(ithprime(i),i=1..1000)]:

%p filter:= proc(n) local L,k;

%p   L:= [seq(P[n] mod P[k],k=1..n-1)];

%p   convert(L,`*`) mod convert(L,`+`) = 0

%p end proc:

%p S:=select(filter, [$2..1000]):

%p map(t -> P[t], S);

%o (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

%Y Cf. A033955, A102647.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jan 11 2021