1,2

LCM of denominators of the coefficients of x^n*z^k in {-ln(1-x)/x}^z as k=0..n, as described by triangle A075264.

Denominators of integer-valued polynomials on prime numbers (with degree n): 1/a(n) is a generator of the ideal formed by the leading coefficients of integer-valued polynomials on prime numbers with degree less than or equal to n.

Also the least common multiple of the orders of all finite subgroups of GL_n(Q) [Minkowski]. Schur's notation for the sequence is M_n = a(n+1). - Martin Lorenz (lorenz(AT)math.temple.edu), May 18 2005

J.-L. Chabert, S.T. Chapman and S.W. Smith, A basis for the ring of polynomials integer-valued on prime numbers, Factorization in integral domains, Lecture Notes in Pure and Appl. Math. 189, Dekker, New York, 1997.

M. Lorenz, Orders of finite groups of matrices, draft, Jun 27 2005

H. Minkowski, Zur Theorie der quadratischen Formen, J. Reine Angew. Math. 101 (1887), 196-202. ( = Ges. Abh., pp. 212-218, Chelsea, New York, 1967.)

I. Schur, Ueber eine Klasse von endlichen Gruppen linearer Substitutionen, Sitzungsber. Preuss. Akad. Wiss. (1905), 77-91. ( = Ges. Abh., Bd. 1, pp. 128-142, Springer-Verlag, Berlin-Heidelberg-New York, 1973.)

(PARI) {a(n)=local(X=x+x^2*O(x^n), D); D=1; for(j=0, n-1, D=lcm(D, denominator( polcoeff(polcoeff((-log(1-X)/x)^z+z*O(z^j), j, z), n-1, x)))); return(D)} (Hanna)

(PARI) {a(n)=prod(i=1, #factor(n!)~, prime(i)^sum(k=0, #binary(n), floor((n-1)/((prime(i)-1)*prime(i)^k))))} (Hanna)

Cf. A002207, A053657, A075264, A075266, A075267.

Adjacent sequences: A053654 A053655 A053656 this_sequence A053658 A053659 A053660

Sequence in context: A111035 A002552 A075265 this_sequence A079608 A068878 A100918

easy,nonn

Jean-Luc Chabert (jlchaber(AT)worldnet.fr), Feb 16 2000

More terms from Paul D. Hanna (pauldhanna(AT)juno.com), Jun 27 2005