cp's OEIS Frontend

A059794 a(n) = n* - 2^(n-1), where n* (A003418) = least common multiple of the numbers [1,...,n].

%I A059794 #18 Jan 26 2015 03:43:06
%S A059794 0,0,2,4,44,28,356,712,2264,2008,26696,25672,356264,352168,343976,
%T A059794 687952,12186704,12121168,232530416,232268272,231743984,230695408,
%U A059794 5350034576,5345840272,26754367184,26737589968,80246324336,80179215472
%N A059794 a(n) = n* - 2^(n-1), where n* (A003418) = least common multiple of the numbers [1,...,n].
%C A059794 It is known that this sequence is always nonnegative - see references.
%C A059794 LCM(1,2,3...n) = n* LCM( binomial(n-1,0), binomial(n-1,1),..., binomial(n-1,n-1)) - see American Mathematical Monthly E2686. - Paul Mills, Feb 14 2002
%D A059794 G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, pp. 12-13, Publications de l'Institut Cartan, 1990.
%H A059794 T. D. Noe, <a href="/A059794/b059794.txt">Table of n, a(n) for n=1..200</a>
%H A059794 Peter L. Montgomery, <a href="http://www.jstor.org/stable/2321959">LCM of Binomial Coefficients, Problem E2686</a>, American Mathematical Monthly, Vol. 86 (1979), p. 131.
%H A059794 M. Nair, <a href="http://www.jstor.org/stable/2320934">On Chebyshev-type inequalities for primes</a>, Amer. Math. Monthly 89 (1982) 126-129.
%H A059794 M. Nair, <a href="http://jlms.oxfordjournals.org/content/s2-25/3/385.extract">A new method in elementary prime number theory</a>, J. London Math. Soc. 25 (1982) 385-391.
%e A059794 Let n=4. Then n*=12 and 2^(4-1)=8. Then we calculate 12-8=4 to be the second term of the sequence.
%p A059794 A059794 := n->lcm(seq(i,i=1..n))-2^(n-1);
%t A059794 a[n_] := LCM @@ Range[n] - 2^(n-1); Table[a[n], {n, 1, 28}] (* _Jean-François Alcover_, Jul 05 2012 *)
%o A059794 (PARI) a(n) = lcm(vector(n, i, i)) - 2^(n-1); \\ _Michel Marcus_, Jan 26 2015
%Y A059794 Cf. A003418, A067068, A068510, A068511.
%K A059794 nice,nonn,easy
%O A059794 1,3
%A A059794 Kathleen Cussen (ehlana52(AT)hotmail.com), Feb 22 2001
%E A059794 Corrected and extended by _Vladeta Jovovic_, Feb 24 2001
%E A059794 References from _Jean-Paul Allouche_, Feb 17 2002