A085542 -id:A085542 - cp's OEIS frontend

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

Offset: 0

MCKAY john (mckay(AT)cs.concordia.ca), Mar 21 2001

sign

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.

Enrique Pérez Herrero, Table of n, a(n) for n = 0..200
Index to sequences related to determinants.

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

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

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

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

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

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

A239682 Product_{i=1..n} A173557(i).

Original entry on oeis.org

1, 1, 2, 2, 8, 16, 96, 96, 192, 768, 7680, 15360, 184320, 1105920, 8847360, 8847360, 141557760, 283115520, 5096079360, 20384317440, 244611809280, 2446118092800, 53814598041600, 107629196083200, 430516784332800, 5166201411993600, 10332402823987200

Offset: 1

Tom Edgar, Mar 24 2014

nonn

This is the generalized factorial for A173557.

			The first five terms of A173557 are 1,1,2,1,4 so a(5)=4*1*2*1*1=8.

Donald E. Knuth and Herbert S. Wilf, The power of a prime that divides a generalized binomial coefficient, J. Reine Angew. Math., 396:212-219, 1989.

Cf. A173557, A085542, A048803.

q=50 # change q for more terms
R=[prod([(x-1) for x in prime_divisors(n)]) for n in [1..q]]
[prod(R[0:i+1]) for i in [0..q-1]]

Product_{i=1..n} A173557(i).

a(n) = abs(A085542(n)).

cp's OEIS Frontend

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

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