A111379 - OEIS

%I #16 Jun 04 2024 01:31:09

%S 68,126,140,162,164,174,204,258,290,294,316,322,392,410,444,456,488,

%T 496,516,550,558,624,654,676,678,688,704,710,732,772,784,790,804,820,

%U 824,830,856,868,908,920,942,948,966,978,984,1030,1038,1060,1068,1098

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

%H Robert Israel, <a href="/A111379/b111379.txt">Table of n, a(n) for n = 1..10000</a>

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

%p q:= 2: count:= 0: R:= NULL:

%p while count < 100 do

%p   p:= q; q:= nextprime(p);

%p   v:= q-p;

%p   m:= max({seq(numtheory:-tau(i),i=p+1 .. q-1)});

%p   S:= select(t -> numtheory:-tau(t) < m, [seq(i*v,i=ceil((p+1)/v) .. floor((q-1)/v))]);

%p   count:= count + nops(S);

%p   R:= R, op(S)

%p od:

%p R; # _Robert Israel_, Jun 03 2024

%Y Cf. A076082, A076083, A113709.

%K nonn

%O 1,1

%A _Leroy Quet_, Nov 07 2005

%E Edited by _Don Reble_, Nov 07 2005