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%I #31 Jan 28 2019 02:09:27
%S 34,1310,203434,16467034,1990586014,41704979954,102099792179230,
%T 22192526378762466
%N a(n) is the smallest number m such that each of the numbers m-1, m and m+1 is a product of n distinct primes.
%C Each term of this sequence is of the form 4k+2.
%H Jacques Tramu, <a href="http://www.primepuzzles.net/puzzles/puzz_371.htm">Puzzle 371</a>
%e a(5)=16467034 because each of the three numbers 16467034-1, 16467034 & 16467034+1 are products of 5 distinct primes (16467033=3*11*17*149*197, 16467034=2*19*23*83*227, 16467035=5*13*37*41*167) and 16467034 is the smallest such number.
%t a[n_] := a[n] = (For[m=1, !(Length[FactorInteger[4m+1]]==n && SquareFreeQ[4m+1] && Length[FactorInteger[4m+2]]==n && SquareFreeQ[4m+2] && Length[FactorInteger[4m+3]]==n && SquareFreeQ[4m+3]), m++ ]; 4m+2); Table[Print[a[n]]; a[n], {n, 2, 6}] (* updated by _Jean-François Alcover_, Jul 04 2013 *)
%o (PARI) a(n)={my(m=1);while(!(issquarefree(m-1)&&issquarefree(m)&&issquarefree(m+1)&&omega(m-1)==n&&omega(m)==n&&omega(m+1)==n),m++);return(m);} main(size)={my(n);return(vector(size,n,a(n+1)));} /* _Anders Hellström_, Jul 14 2015 */
%Y Cf. A093549, A052215, A093548, A248201, A248202, A248203, A248204, A259349, A259350, A259801.
%K more,nonn
%O 2,1
%A _Farideh Firoozbakht_, Apr 07 2004, corrected Aug 26 2006
%E a(7) added from Jacques Tramu's web site by _Farideh Firoozbakht_, Aug 26 2006
%E a(8) from _Donovan Johnson_, Oct 27 2008
%E a(9) from _James G. Merickel_, Jul 24 2015
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