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%I #54 Aug 28 2023 08:29:11
%S 2,2,3,7,13,61,61,421,841,2521,2521,27721,27721,360361,360361,360361,
%T 720721,12252241,12252241,232792561,232792561,232792561,232792561,
%U 5354228881,5354228881,26771144401,26771144401,80313433201,80313433201
%N a(n) = 1 + lcm(1, 2, ..., n) = 1 + A003418(n).
%C Consider the triangle in which the n-th row contains the second run of n consecutive numbers such that the r-th term is divisible by r. Sequence gives the first column of the triangle. The first run trivially begins with 1.
%C Also the smallest of n consecutive integers (with the first greater than 1) divisible respectively by 1, 2, 3, ..., n. - _Robert G. Wilson v_, Oct 30 2014
%C Also the smallest number m > 1 such that m == 1 (mod i) for all 1 <= i <= n. - _Franz Vrabec_, Aug 18 2023
%F a(n) = 1 + A003418(n).
%e First column of the triangle A075061:
%e 2;
%e 3, 4;
%e 7, 8, 9;
%e 13, 14, 15, 16;
%e 61, 62, 63, 64, 65;
%e 61, 62, 63, 64, 65, 66;
%e ...
%t Table[LCM@@Range[n] + 1, {n, 30}] (* _Harvey P. Dale_, Nov 15 2011 *)
%o (Magma) [Exponent(SymmetricGroup(n))+1 : n in [1..30]]; // _Vincenzo Librandi_, Oct 31 2014
%o (PARI) a(n)=lcm([1..n])+1 \\ _Charles R Greathouse IV_, Nov 04 2014
%Y Cf. A003418, A060401, A065500, A070198, A072562, A075061, A249051.
%K nonn
%O 0,1
%A _Amarnath Murthy_, Sep 08 2002
%E New definition from _Vladeta Jovovic_, Jun 16 2003
%E Edited by _N. J. A. Sloane_, Jul 01 2008 at the suggestion of _R. J. Mathar_
%E a(0)=2 prepended by _Max Alekseyev_, Sep 04 2015
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