A060238 a(n) = det(M) where M is an n X n matrix with M[i,j] = lcm(i,j).

1, 1, -2, 12, -48, 960, 11520, -483840, 3870720, -69672960, -2786918400, 306561024000, 7357464576000, -1147764473856000, -96412215803904000, -11569465896468480000, 185111454343495680000, -50350315581430824960000, -1812611360931509698560000, 619913085438576316907520000

Offset

0,3

References

J.-M. De Koninck & A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Problème 695, pp. 90, 297-298, Ellipses, Paris, 2004.

J. Sandor and B. Crstici, Handbook of Number Theory II, Springer, 2004, p. 265, eq. 10.

Links

Enrique Pérez Herrero, Table of n, a(n) for n = 0..200

Jorma K. Merikoski, Pentti Haukkanen, Antonio Sasaki, and Timo Tossavainen, On Generalized Eigenvalues of MAX Matrices to MIN Matrices and LCM Matrices to GCD Matrices, J. Int. Seq. (2025) Vol. 28, Art. 25.7.1.

Index to sequences related to determinants.

Formula

For n >= 2, a(n) = n! * Product_{j=2..n} Product_{p|j} (1-p) (where the second product is over all primes p that divide j) (cf. A023900). - Avi Peretz (njk(AT)netvision.net.il), Mar 22 2001

a(n) = n! * Product_{p<=n} (1-p)^floor(n/p) where the product runs through the primes. - Benoit Cloitre, Jan 31 2008

a(n) = A000142(n) * A085542(n). - Enrique Pérez Herrero, Jun 08 2010

a(n) = A001088(n) * A048803(n) * (-1)^A013939(n). - Amiram Eldar, Dec 19 2018

a(n) = Product_{k=1..n} (-1)^A001221(k) * A000010(k) * A007947(k) [De Koninck & Mercier]. - Bernard Schott, Dec 11 2020

Maple

A060238:=n->n!*mul((1-ithprime(i))^floor(n/ithprime(i)), i=1..numtheory[pi](n)): seq(A060238(n), n=0..20); # Wesley Ivan Hurt, Aug 15 2016

Mathematica

A060238[n_]:=n!*Product[(1 - Prime[i])^Floor[n/Prime[i]], {i, PrimePi[n]}]; Array[A060238, 20] (* Enrique Pérez Herrero, Jun 08 2010 *)

Prog

(PARI) a(n)=n!*prod(p=1, sqrtint(n), if(isprime(p), (1-p)^floor(n/p), 1)) \\ Benoit Cloitre, Jan 31 2008

Crossrefs

Cf. A000142, A001088, A013939, A023900, A048803, A060239, A085542.

Sequence in context: A277183 A052588 A139239 * A085495 A119978 A139234

Adjacent sequences: A060235 A060236 A060237 * A060239 A060240 A060241

Keyword

sign

Author

John McKay (mckay(AT)cs.concordia.ca), Mar 21 2001

Extensions

a(0)=1 prepended by Alois P. Heinz, Jan 25 2023

Status

approved