A264664 a(1)=210; for n > 1, a(n) is the least integer not occurring earlier such that a(n) shares exactly four distinct prime divisors with a(n-1).

210, 420, 630, 840, 1050, 1260, 1470, 1680, 1890, 2100, 2310, 330, 660, 990, 1320, 1650, 1980, 2640, 2970, 3300, 3630, 3960, 4290, 390, 780, 1170, 1560, 1950, 2340, 2730, 546, 1092, 1638, 2184, 3276, 3822, 4368, 4914, 5460, 910, 1820, 3640, 4550, 6370, 7280

Offset: 1

Author

Michel Lagneau, Nov 20 2015

Keywords

• nonn

Comments

The first odd term is a(47) = 1365. - Michel Marcus, Nov 21 2015

Examples

			630 is in the sequence because the common prime distinct divisors between a(2)=420 and a(3)=630 are 2, 3, 5 and 7.
		

Links

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

Crossrefs

Cf. A246946, A246947.

Programs

Maple

with(numtheory):a0:={2, 3, 5, 7}:lst:={}:
for n from 1 to 100 do:
  ii:=0:
    for k from 210 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)=4
          then
          printf(`%d, `, k):lst:=lst union {k}:a0:=lst1:ii:=1:
         else
         fi:
      od:
  od:

Mathematica

a = {210}; Do[k = 1; While[Nand[! MemberQ[a, k], Length@ Intersection[First /@ FactorInteger@ a[[n - 1]], First /@ FactorInteger@ k] == 4], k++]; AppendTo[a, k], {n, 2, 45}]; a (* Michael De Vlieger, Nov 21 2015 *)