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A246947 a(1)=30; for n > 1, a(n) is the least integer not occurring earlier such that a(n) shares exactly three distinct prime divisors with a(n-1).

%I A246947 #16 Nov 25 2015 21:43:53
%S A246947 30,60,90,120,150,180,210,42,84,126,168,252,294,336,378,420,70,140,
%T A246947 280,350,490,560,630,105,315,525,735,840,240,270,300,330,66,132,198,
%U A246947 264,396,462,154,308,616,770,110,220,440,550,660,165,495,825,990,360,390,78
%N A246947 a(1)=30; for n > 1, a(n) is the least integer not occurring earlier such that a(n) shares exactly three distinct prime divisors with a(n-1).
%C A246947 All terms belong to A000977. Is this a permutation of A000977? - _Michel Marcus_, Nov 24 2015
%H A246947 Michel Lagneau, <a href="/A246947/b246947.txt">Table of n, a(n) for n = 1..2000</a>
%e A246947 90 is in the sequence because the common prime distinct divisors between a(2)=60 and a(3)=90 are 2, 3 and 5.
%p A246947 with(numtheory):a0:={2,3,5}:lst:={}:
%p A246947 for n from 1 to 100 do:
%p A246947   ii:=0:
%p A246947     for k from 30 to 50000 while(ii=0) do:
%p A246947       y:=factorset(k):n0:=nops(y):lst1:={}:
%p A246947         for j from 1 to n0 do:
%p A246947         lst1:=lst1 union {y[j]}:
%p A246947         od:
%p A246947          a1:=a0 intersect lst1:
%p A246947          if {k} intersect lst ={} and a1 <> {} and nops(a1)=3
%p A246947           then
%p A246947           printf(`%d, `,k):lst:=lst union {k}:a0:=lst1:ii:=1:
%p A246947          else
%p A246947          fi:
%p A246947       od:
%p A246947   od:
%t A246947 f[s_List]:=Block[{m=s[[-1]],k=30},While[MemberQ[s,k]||Intersection[Transpose[FactorInteger[k]][[1]],Transpose[FactorInteger[m]][[1]]]=={}|| Length[Intersection[Transpose[FactorInteger[k]][[1]],Transpose[FactorInteger[m]][[1]]]]!=3,k++];Append[s,k]];Nest[f,{30},70]
%o A246947 (PARI) lista(nn) = {a = 30; print1(a, ", "); fa = (factor(a)[,1])~; va = [a]; k = 0; while (k!= nn, k = 1; while (!((#setintersect(fa, (factor(k)[,1])~) == 3) && (! vecsearch(va, k))), k++); a = k; print1(a, ", "); fa = (factor(a)[,1])~; va = vecsort(concat(va, k)););} \\ _Michel Marcus_, Nov 24 2015
%Y A246947 Cf. A000977, A064413, A246946.
%K A246947 nonn
%O A246947 1,1
%A A246947 _Michel Lagneau_, Sep 08 2014