A076082 -id:A076082 - cp's OEIS frontend

A076083 Consider all composite numbers between prime(n) and prime(n+1); take those with smallest number of divisors; a(n) is the smallest of them.

4, 6, 9, 12, 14, 18, 21, 25, 30, 33, 38, 42, 46, 49, 55, 60, 62, 69, 72, 74, 82, 85, 91, 98, 102, 106, 108, 111, 121, 129, 133, 138, 141, 150, 155, 158, 166, 169, 177, 180, 183, 192, 194, 198, 201, 213, 226, 228, 230, 235, 240, 247, 253, 259, 265, 270, 274, 278

Offset: 2

Amarnath Murthy, Oct 07 2002

nonn

Harvey P. Dale, Table of n, a(n) for n = 2..1000

Cf. A076082.

snd[lst_]:=First[SortBy[lst,DivisorSigma[0,#]&]]; snd/@(Range[#[[1]]+1, #[[2]]- 1]&/@Partition[Prime[Range[2,60]],2,1]) (* Harvey P. Dale, Jul 06 2014 *)

for(n=2,100,m=99999:r=0:for(k=prime(n)+1, prime(n+1)-1,if(!isprime(k),if(numdiv(k)

More terms from Ralf Stephan, Mar 23 2003

A097619 Numbers having more prime factors than each of their neighbors.

Original entry on oeis.org

4, 6, 8, 12, 16, 18, 20, 24, 30, 32, 36, 40, 42, 48, 50, 52, 54, 56, 60, 64, 66, 68, 70, 72, 78, 80, 84, 88, 90, 92, 96, 100, 102, 104, 108, 110, 112, 114, 120, 126, 128, 130, 132, 138, 140, 144, 150, 152, 156, 160, 162, 168, 176, 180, 182, 184, 186, 189, 192, 196

Offset: 1

Reinhard Zumkeller, Aug 17 2004

nonn

Even terms are much more frequent. Among first 10000 terms exactly 612 are odd. First odd terms are 189, 243, 315, 405, 525, 567, 675; corresponding indices are 58, 77, 102, 130, 169, 182, 216. - Zak Seidov, Mar 06 2015

			A001222(50)=A001222(2*5*5)=3 > A001222(50-1)=A001222(7*7)=2 and A001222(50) > A001222(50+1)=A001222(3*17)=2, therefore 50 is a term.

Zak Seidov, Table of n, a(n) for n = 1..10000

Cf. A097620, A076082, A001222.

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

A076083 Consider all composite numbers between prime(n) and prime(n+1); take those with smallest number of divisors; a(n) is the smallest of them.

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A097619 Numbers having more prime factors than each of their neighbors.

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

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