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
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.
Programs
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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
Comments