A114331 Observe that A052248(n) = greatest prime divisor q (say) of all composite numbers between p = prime(n) and next prime. There is only one composite number in this range which is divisible by q. Sequence lists these composite numbers.

4, 6, 10, 12, 14, 18, 22, 26, 30, 34, 38, 42, 46, 51, 58, 60, 62, 69, 72, 74, 82, 86, 94, 99, 102, 106, 108, 111, 122, 129, 134, 138, 146, 150, 155, 158, 166, 172, 178, 180, 183, 192, 194, 198, 206, 218, 226, 228, 232, 237, 240, 249, 254, 262, 267, 270

Offset: 2

Author

N. J. A. Sloane, based on correspondence from Leroy Quet and Hugo Pfoertner, Feb 22 2006

Keywords

• nonn

Comments

The uniqueness follows from generalization of Bertrand's Postulate. - Franklin T. Adams-Watters.

Links

• Robert Israel, Table of n, a(n) for n = 2..10000
• Eric Weisstein's World of Mathematics, Bertrand's Postulate

Crossrefs

Cf. A052248, A114349.

Programs

Maple

p:= 3: R:= NULL:
for i from 2 to 100 do
  pp:= p; p:= nextprime(p);
  rmax:= 0:
  for q from pp+1 to p-1 do
    r:= max(numtheory:-factorset(q));
    if r > rmax then rmax:= r; qmax:= q fi
  od;
  R:= R, qmax
od:
R; # Robert Israel, Apr 01 2021