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

%I A060238 #43 Jan 25 2023 17:47:59
%S A060238 1,1,-2,12,-48,960,11520,-483840,3870720,-69672960,-2786918400,
%T A060238 306561024000,7357464576000,-1147764473856000,-96412215803904000,
%U A060238 -11569465896468480000,185111454343495680000,-50350315581430824960000,-1812611360931509698560000
%N A060238 a(n) = det(M) where M is an n X n matrix with M[i,j] = lcm(i,j).
%D A060238 J.-M. De Koninck & A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Problème 695, pp. 90, 297-298, Ellipses, Paris, 2004.
%D A060238 J. Sandor and B. Crstici, Handbook of Number Theory II, Springer, 2004, p. 265, eq. 10.
%H A060238 Enrique Pérez Herrero, <a href="/A060238/b060238.txt">Table of n, a(n) for n = 0..200</a>
%H A060238 <a href="/index/De#determinants">Index to sequences related to determinants</a>.
%F A060238 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
%F A060238 a(n) = n! * Product_{p<=n} (1-p)^floor(n/p) where the product runs through the primes. - _Benoit Cloitre_, Jan 31 2008
%F A060238 a(n) = A000142(n) * A085542(n). - _Enrique Pérez Herrero_, Jun 08 2010
%F A060238 a(n) = A001088(n) * A048803(n) * (-1)^A013939(n). - _Amiram Eldar_, Dec 19 2018
%F A060238 a(n) = Product_{k=1..n} (-1)^A001221(k) * A000010(k) * A007947(k) [De Koninck & Mercier]. - _Bernard Schott_, Dec 11 2020
%p A060238 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
%t A060238 A060238[n_]:=n!*Product[(1 - Prime[i])^Floor[n/Prime[i]], {i, PrimePi[n]}]; Array[A060238, 20] (* _Enrique Pérez Herrero_, Jun 08 2010 *)
%o A060238 (PARI) a(n)=n!*prod(p=1,sqrtint(n),if(isprime(p),(1-p)^floor(n/p),1)) \\ _Benoit Cloitre_, Jan 31 2008
%Y A060238 Cf. A000142, A001088, A013939, A023900, A048803, A060239, A085542.
%K A060238 sign
%O A060238 0,3
%A A060238 MCKAY john (mckay(AT)cs.concordia.ca), Mar 21 2001
%E A060238 a(0)=1 prepended by _Alois P. Heinz_, Jan 25 2023