cp's OEIS Frontend

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

%I A111379 #16 Jun 04 2024 01:31:09
%S A111379 68,126,140,162,164,174,204,258,290,294,316,322,392,410,444,456,488,
%T A111379 496,516,550,558,624,654,676,678,688,704,710,732,772,784,790,804,820,
%U A111379 824,830,856,868,908,920,942,948,966,978,984,1030,1038,1060,1068,1098
%N A111379 Composite numbers n which are divisible by (nextprime(n) - prevprime(n)), but have fewer divisors than some number between those two primes.
%H A111379 Robert Israel, <a href="/A111379/b111379.txt">Table of n, a(n) for n = 1..10000</a>
%e A111379 68 is there because it is divisible by (71-67), but 70 has more divisors.
%p A111379 q:= 2: count:= 0: R:= NULL:
%p A111379 while count < 100 do
%p A111379   p:= q; q:= nextprime(p);
%p A111379   v:= q-p;
%p A111379   m:= max({seq(numtheory:-tau(i),i=p+1 .. q-1)});
%p A111379   S:= select(t -> numtheory:-tau(t) < m, [seq(i*v,i=ceil((p+1)/v) .. floor((q-1)/v))]);
%p A111379   count:= count + nops(S);
%p A111379   R:= R, op(S)
%p A111379 od:
%p A111379 R; # _Robert Israel_, Jun 03 2024
%Y A111379 Cf. A076082, A076083, A113709.
%K A111379 nonn
%O A111379 1,1
%A A111379 _Leroy Quet_, Nov 07 2005
%E A111379 Edited by _Don Reble_, Nov 07 2005