A349738 Numbers k such that A255217(k) divides A002110(k).

2, 4, 5, 9, 15, 17, 20, 24, 25, 26, 27, 29, 31, 32, 33, 34, 37, 44, 45, 46, 49, 51, 52, 61, 62, 63, 64, 71, 74, 79, 80, 81, 82, 85, 87, 88, 91, 95, 103, 104, 105, 110, 111, 112, 115, 117, 118, 119, 120, 121, 127, 131, 135, 137, 142, 148, 150, 152, 154, 158, 159, 163, 165, 173, 175, 177, 179, 181

Offset: 1

Author

J. M. Bergot and Robert Israel, Nov 28 2021

Keywords

• nonn

Examples

			a(3) = 5 is a term because A255217(5) = 2*3*5*7*11 mod (2+3+5+7+11) = 14 divides 2*3*5*7*11.
		

Links

• Martin Ehrenstein, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A007504, A255217. Contains A349734.

Programs

Maple

P:= 1: S:= 0: p:= 1:
count:= 0: R:= NULL:
for n from 1 while count < 100 do
  p:= nextprime(p);
  P:= P*p; S:= S+p;
  r:= P mod S;
  if r = 0 then next fi;
  v:= P mod r;
  if v = 0 then
    count:= count+1; R:= R,n;
  fi
od:
R;

Mathematica

Select[Range[200], (m = Mod[Times @@ (p = Prime[Range[#]]), Plus @@ p]) > 0 && Divisible[Times @@ p, m] &] (* Amiram Eldar, Nov 28 2021 *)