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

0, 0, 2, 4, 44, 28, 356, 712, 2264, 2008, 26696, 25672, 356264, 352168, 343976, 687952, 12186704, 12121168, 232530416, 232268272, 231743984, 230695408, 5350034576, 5345840272, 26754367184, 26737589968, 80246324336, 80179215472

Offset

1,3

Comments

It is known that this sequence is always nonnegative - see references.

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

References

G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, pp. 12-13, Publications de l'Institut Cartan, 1990.

Links

T. D. Noe, Table of n, a(n) for n=1..200

Peter L. Montgomery, LCM of Binomial Coefficients, Problem E2686, American Mathematical Monthly, Vol. 86 (1979), p. 131.

M. Nair, On Chebyshev-type inequalities for primes, Amer. Math. Monthly 89 (1982) 126-129.

M. Nair, A new method in elementary prime number theory, J. London Math. Soc. 25 (1982) 385-391.

Example

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.

Maple

A059794 := n->lcm(seq(i, i=1..n))-2^(n-1);

Mathematica

a[n_] := LCM @@ Range[n] - 2^(n-1); Table[a[n], {n, 1, 28}] (* Jean-François Alcover, Jul 05 2012 *)

Prog

(PARI) a(n) = lcm(vector(n, i, i)) - 2^(n-1); \\ Michel Marcus, Jan 26 2015

Crossrefs

Cf. A003418, A067068, A068510, A068511.

Sequence in context: A009717 A018317 A359876 * A116611 A141142 A353797

Adjacent sequences: A059791 A059792 A059793 * A059795 A059796 A059797

Keyword

nice,nonn,easy

Author

Kathleen Cussen (ehlana52(AT)hotmail.com), Feb 22 2001

Extensions

Corrected and extended by Vladeta Jovovic, Feb 24 2001

References from Jean-Paul Allouche, Feb 17 2002

Status

approved