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A136742 Product of the n-th run of squarefree numbers.

%I A136742 #13 Feb 16 2025 08:33:07
%S A136742 6,210,110,2730,17,19,10626,26,26970,39270,54834,74046,2162,51,53,55,
%T A136742 195054,3782,287430,342930,5402,474474,6806,635970,89,91,830490,97,
%U A136742 1061106,1190910,1330890,1481430,14042,15006,127,2196870,17822,2627934
%N A136742 Product of the n-th run of squarefree numbers.
%C A136742 All terms are squarefree;
%C A136742 a(n) mod A072284(n) = 0;
%C A136742 A136743(n) = A001221(a(n)).
%H A136742 Robert Israel, <a href="/A136742/b136742.txt">Table of n, a(n) for n = 1..10000</a>
%H A136742 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Squarefree.html">Squarefree</a>
%F A136742 a(n) = Product_{k=0..A120992(n)-1} (A072284(n)+k).
%e A136742 n=10: A072284(10)=33, A120992(10)=3: a(10)=33*34*35=39270.
%p A136742 R:= NULL:
%p A136742 state:= false:
%p A136742 count:= 0:
%p A136742 for n from 1 while count < 100 do
%p A136742 if numtheory:-issqrfree(n) then
%p A136742      if state then P:= P*n
%p A136742      else P:= n; state:= true
%p A136742      fi
%p A136742   elif state then
%p A136742      R:= R, P;
%p A136742      count:= count+1;
%p A136742      state:= false
%p A136742   fi
%p A136742 od:
%p A136742 R; # _Robert Israel_, Jan 06 2020
%t A136742 Times @@ # & /@ DeleteCases[#, _?(! SquareFreeQ@ First@ # &)] &@ SplitBy[Range[140], SquareFreeQ] (* _Michael De Vlieger_, Jan 06 2020 *)
%Y A136742 Cf. A005117.
%K A136742 nonn
%O A136742 1,1
%A A136742 _Reinhard Zumkeller_, Jan 20 2008