login
A111379
Composite numbers n which are divisible by (nextprime(n) - prevprime(n)), but have fewer divisors than some number between those two primes.
2
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
1,1
LINKS
EXAMPLE
68 is there because it is divisible by (71-67), but 70 has more divisors.
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Nov 07 2005
EXTENSIONS
Edited by Don Reble, Nov 07 2005
STATUS
approved