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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).

2

`%I #11 Nov 21 2015 22:49:11
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`%S 210,420,630,840,1050,1260,1470,1680,1890,2100,2310,330,660,990,1320,
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`%T 1650,1980,2640,2970,3300,3630,3960,4290,390,780,1170,1560,1950,2340,
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`%U 2730,546,1092,1638,2184,3276,3822,4368,4914,5460,910,1820,3640,4550,6370,7280
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`%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).
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`%C The first odd term is a(47) = 1365. - _Michel Marcus_, Nov 21 2015
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`%H Michel Lagneau, <a href="/A264664/b264664.txt">Table of n, a(n) for n = 1..2000</a>
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`%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.
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`%p with(numtheory):a0:={2, 3, 5, 7}:lst:={}:
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`%p for n from 1 to 100 do:
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`%p ii:=0:
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`%p for k from 210 to 50000 while(ii=0) do:
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`%p y:=factorset(k):n0:=nops(y):lst1:={}:
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`%p for j from 1 to n0 do:
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`%p lst1:=lst1 union {y[j]}:
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`%p od:
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`%p a1:=a0 intersect lst1:
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`%p if {k} intersect lst ={} and a1 <> {} and nops(a1)=4
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`%p then
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`%p printf(`%d, `, k):lst:=lst union {k}:a0:=lst1:ii:=1:
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`%p else
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`%p fi:
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`%p od:
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`%p od:
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`%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 *)
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`%Y Cf. A246946, A246947.
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`%K nonn
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`%O 1,1
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`%A _Michel Lagneau_, Nov 20 2015
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