A076083 -id:A076083 - cp's OEIS frontend

A076082 Consider all composite numbers between prime(n) and prime(n+1); take those with greatest number of divisors; a(n) is the smallest of them.

4, 6, 8, 12, 16, 18, 20, 24, 30, 36, 40, 42, 44, 48, 54, 60, 66, 70, 72, 78, 80, 84, 90, 100, 102, 104, 108, 112, 120, 128, 132, 138, 144, 150, 156, 160, 165, 168, 176, 180, 182, 192, 196, 198, 210, 216, 224, 228, 230, 234, 240, 246, 252, 260, 264, 270, 276, 280

Offset: 2

Amarnath Murthy, Oct 07 2002

nonn

Cf. A076083.

for(n=2,100,m=0:r=0:for(k=prime(n)+1, prime(n+1)-1,if(!isprime(k),if(numdiv(k)>m,r=k:m=numdiv(k)))):print1(r","))

Corrected and extended by Ralf Stephan, Mar 23 2003

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

Original entry on oeis.org

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

Leroy Quet, Nov 07 2005

nonn

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

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

Cf. A076082, A076083, A113709.

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

Edited by Don Reble, Nov 07 2005

cp's OEIS Frontend

A076082 Consider all composite numbers between prime(n) and prime(n+1); take those with greatest number of divisors; a(n) is the smallest of them.

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