A264718 a(1)=2310; for n > 1, a(n) is the least integer not occurring earlier such that a(n) shares exactly five distinct prime divisors with a(n-1).

2310, 4620, 6930, 9240, 11550, 13860, 16170, 18480, 20790, 23100, 25410, 27720, 30030, 2730, 5460, 8190, 10920, 13650, 16380, 19110, 21840, 24570, 27300, 32760, 35490, 38220, 40950, 43680, 46410, 3570, 7140, 10710, 14280, 17850, 21420, 24990, 28560, 32130

Offset: 1

Author

Michel Lagneau, Nov 21 2015

Keywords

• nonn

Comments

The first term a(1) = 2*3*5*7*11.

Examples

			46410 is in the sequence because the distinct prime divisors common to a(29) = 46410 = 2*3*5*7*13*17 and a(28) = 43680 = 2^5*3*5*7*13 are 2, 3, 5, 7 and 13.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A246946, A246947, A264664.

Programs

Maple

with(numtheory):a0:={2, 3, 5, 7, 11}:lst:={}:
for n from 1 to 100 do:
  ii:=0:
    for k from 2310 to 50000 while(ii=0) do:
      y:=factorset(k):n0:=nops(y):lst1:={}:
        for j from 1 to n0 do:
        lst1:=lst1 union {y[j]}:
        od:
         a1:=a0 intersect lst1:
         if {k} intersect lst ={} and a1 <> {} and nops(a1)=5
          then
          printf(`%d, `, k):lst:=lst union {k}:a0:=lst1:ii:=1:
         else
         fi:
      od:
  od:

Mathematica

a = {2310}; Do[k = 1; While[Nand[! MemberQ[a, k], Length@ Intersection[First /@ FactorInteger@ a[[n - 1]], First /@ FactorInteger@ k] == 5], k++]; AppendTo[a, k], {n, 2, 38}]; a (* Michael De Vlieger, Nov 21 2015 *)