A111379 Composite numbers n which are divisible by (nextprime(n) - prevprime(n)), but have fewer divisors than some number between those two primes.

68, 126, 140, 162, 164, 174, 204, 258, 290, 294, 316, 322, 392, 410, 444, 456, 488, 496, 516, 550, 558, 624, 654, 676, 678, 688, 704, 710, 732, 772, 784, 790, 804, 820, 824, 830, 856, 868, 908, 920, 942, 948, 966, 978, 984, 1030, 1038, 1060, 1068, 1098

Offset: 1

Author

Leroy Quet, Nov 07 2005

Keywords

• nonn

Examples

			68 is there because it is divisible by (71-67), but 70 has more divisors.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A076082, A076083, A113709.

Programs

Maple

q:= 2: count:= 0: R:= NULL:
while count < 100 do
  p:= q; q:= nextprime(p);
  v:= q-p;
  m:= max({seq(numtheory:-tau(i),i=p+1 .. q-1)});
  S:= select(t -> numtheory:-tau(t) < m, [seq(i*v,i=ceil((p+1)/v) .. floor((q-1)/v))]);
  count:= count + nops(S);
  R:= R, op(S)
od:
R; # Robert Israel, Jun 03 2024

Extensions

Edited by Don Reble, Nov 07 2005