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%I #38 Nov 16 2014 14:48:43
%S 2,3,7,13,0,61,421,841,0,2521,0,27721,0,0,360361,720721,0,12252241,0,
%T 0,0,232792561,0,5354228881,0,26771144401,0,80313433201,0,
%U 2329089562801,72201776446801,0,0,0,0,144403552893601,0,0,0,5342931457063201,0
%N The smallest integer > 1 of exactly n consecutive integers divisible respectively by the first n natural numbers (A000027), or 0 if no such number exists.
%C For all n > 1 and a(n) # 0, a(n) == 1 (mod p#), where p# are the primorial numbers (A034386).
%C When a(n) is not 0, a(n) = A075059(n).
%C a(n) = 0 when n is a member of A080765.
%e a(3) = 7 because the smallest k such that 1|k, 2|k+1, 3|k+2, and 4 does not divide k+3 is 7.
%e a(4) = 13 because the smallest k such that 1|k, 2|k+1, 3|k+2, 4|k+3, and 5 does not divide k+4 is 13.
%t f[n_] := Block[{lcm = LCM @@ Range@ n}, If[ lcm == LCM @@ Range[n + 1], 0, lcm + 1]]; Array[ f, 42] (* _Robert G. Wilson v_, Nov 13 2014 *)
%Y Cf. A075059, A034386, A080765.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Oct 30 2014
%E a(5) corrected (0, not 181) by _Jon Perry_, Nov 05 2014
%E Sequence corrected by _Robert G. Wilson v_, Nov 13 2014
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