A068511 -id:A068511 - cp's OEIS frontend

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

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

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

			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.

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

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.

Cf. A003418, A067068, A068510, A068511.

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

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

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

Corrected and extended by Vladeta Jovovic, Feb 24 2001

References from Jean-Paul Allouche, Feb 17 2002

A068510 a(n) = lcm(1,...,n) - (product of primes <= n).

Original entry on oeis.org

0, 0, 0, 6, 30, 30, 210, 630, 2310, 2310, 25410, 25410, 330330, 330330, 330330, 690690, 11741730, 11741730, 223092870, 223092870, 223092870, 223092870, 5131136010, 5131136010, 26548051530, 26548051530, 80090340330, 80090340330

Offset: 1

N. J. A. Sloane, Mar 21 2002

Tenenbaum, G. (2015). Introduction to analytic and probabilistic number theory, 3rd ed., American Mathematical Soc. See page 22.

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

Cf. A059794, A068511.

a[1] := 0:a[2] := 0:l := 2:p := 3:pp := 2:for i from 3 to 50 do l := ilcm(l,i): if(p=i) then pp := pp*p:p := nextprime(p):end if: a[i] := l-pp:end do:q := seq(a[j],j=1..50);

f[n_] := (LCM @@ Table[i, {i, n}] - Product[Prime[i], {i, PrimePi[n]}]); Table[f[n], {n, 30}]

More terms from Sascha Kurz, Mar 23 2002

cp's OEIS Frontend

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

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