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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).

%I A264718 #10 Nov 25 2015 21:03:32
%S A264718 2310,4620,6930,9240,11550,13860,16170,18480,20790,23100,25410,27720,
%T A264718 30030,2730,5460,8190,10920,13650,16380,19110,21840,24570,27300,32760,
%U A264718 35490,38220,40950,43680,46410,3570,7140,10710,14280,17850,21420,24990,28560,32130
%N 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).
%C A264718 The first term a(1) = 2*3*5*7*11.
%H A264718 Michel Lagneau, <a href="/A264718/b264718.txt">Table of n, a(n) for n = 1..2000</a>
%e A264718 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.
%p A264718 with(numtheory):a0:={2, 3, 5, 7, 11}:lst:={}:
%p A264718 for n from 1 to 100 do:
%p A264718   ii:=0:
%p A264718     for k from 2310 to 50000 while(ii=0) do:
%p A264718       y:=factorset(k):n0:=nops(y):lst1:={}:
%p A264718         for j from 1 to n0 do:
%p A264718         lst1:=lst1 union {y[j]}:
%p A264718         od:
%p A264718          a1:=a0 intersect lst1:
%p A264718          if {k} intersect lst ={} and a1 <> {} and nops(a1)=5
%p A264718           then
%p A264718           printf(`%d, `, k):lst:=lst union {k}:a0:=lst1:ii:=1:
%p A264718          else
%p A264718          fi:
%p A264718       od:
%p A264718   od:
%t A264718 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 *)
%Y A264718 Cf. A246946, A246947, A264664.
%K A264718 nonn
%O A264718 1,1
%A A264718 _Michel Lagneau_, Nov 21 2015