A087977 a(n) is the first term in the first chain of at least n consecutive numbers each having exactly four distinct prime factors.

210, 7314, 37960, 134043, 357642, 1217250, 1217250, 14273478, 44939642, 76067298, 163459742, 547163235, 2081479430, 2771263512, 11715712410, 17911205580, 56608713884, 118968284928, 118968284928, 585927201062, 585927201062, 585927201062, 585927201062

Offset: 1

Author

Labos Elemer, Sep 26 2003

Keywords

• nonn
• fini

Comments

Eggleton and MacDougall show that there are no more than 419 terms in this sequence. - T. D. Noe, Oct 13 2008

a(28) > 2 * 10^15. - Toshitaka Suzuki, Jun 22 2025

Examples

			a(6) = a(7) = 1217250 because the relevant 7 successive numbers have 4 distinct prime factors:
  1217250 = 2   *  3^2 *   5^3 * 541;
  1217251 = 7   * 17   *  53   * 193;
  1217252 = 2^2 * 23   * 101   * 131;
  1217253 = 3   * 47   *  89   *  97;
  1217254 = 2   * 19   * 103   * 311;
  1217255 = 5   * 13   *  61   * 307;
  1217256 = 2^3 *  3   *  67   * 757.
		

Links

• Toshitaka Suzuki, Table of n, a(n) for n = 1..27 (terms 1..23 from Donovan Johnson).
• Roger B. Eggleton and James A. MacDougall, Consecutive integers with equally many principal divisors, Math. Mag. 81 (2008), 235-248.

Crossrefs

Cf. A080569 (m=3), A064708 (m=2).

Cf. A087978, A138206, A138207, A154573.

Programs

Mathematica

k=1; Do[While[Union[Table[Length[FactorInteger[i]], {i, k, k+n-1}]]!={4}, k++ ]; Print[k], {n, 1, 8}]
Module[{d4=Table[If[PrimeNu[n]==4,1,0],{n,143*10^5}]},Flatten[Table[ SequencePosition[d4,PadRight[{},n,1],1],{n,8}],1][[All,1]]] (* Requires Mathematica version 10 or later *) (* This generates the first 8 terms of the sequence *) (* Harvey P. Dale, Aug 25 2017 *)

Extensions

More terms from Don Reble, Sep 29 2003

a(13)-a(19) from Donovan Johnson, Mar 06 2008

a(20)-a(23) from Donovan Johnson, Jan 15 2009