A264664 - OEIS

%I #11 Nov 21 2015 22:49:11

%S 210,420,630,840,1050,1260,1470,1680,1890,2100,2310,330,660,990,1320,

%T 1650,1980,2640,2970,3300,3630,3960,4290,390,780,1170,1560,1950,2340,

%U 2730,546,1092,1638,2184,3276,3822,4368,4914,5460,910,1820,3640,4550,6370,7280

%N 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).

%C The first odd term is a(47) = 1365. - _Michel Marcus_, Nov 21 2015

%H Michel Lagneau, <a href="/A264664/b264664.txt">Table of n, a(n) for n = 1..2000</a>

%e 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.

%p with(numtheory):a0:={2, 3, 5, 7}:lst:={}:

%p for n from 1 to 100 do:

%p   ii:=0:

%p     for k from 210 to 50000 while(ii=0) do:

%p       y:=factorset(k):n0:=nops(y):lst1:={}:

%p         for j from 1 to n0 do:

%p         lst1:=lst1 union {y[j]}:

%p         od:

%p          a1:=a0 intersect lst1:

%p          if {k} intersect lst ={} and a1 <> {} and nops(a1)=4

%p           then

%p           printf(`%d, `, k):lst:=lst union {k}:a0:=lst1:ii:=1:

%p          else

%p          fi:

%p       od:

%p   od:

%t 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 *)

%Y Cf. A246946, A246947.

%K nonn

%O 1,1

%A _Michel Lagneau_, Nov 20 2015