The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A071248 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A071248

a(n) = Product_{k=1..n} lcm(n,k).
(history; published version)

#19 by Harvey P. Dale at Wed Jun 12 16:06:34 EDT 2019

STATUS

editing

approved

#18 by Harvey P. Dale at Wed Jun 12 16:06:30 EDT 2019

MATHEMATICA

Table[Product[LCM[k, n], {k, n}], {n, 20}] (* Harvey P. Dale, Jun 12 2019 *)

STATUS

approved

editing

#17 by R. J. Mathar at Sat Mar 11 14:42:09 EST 2017

STATUS

editing

approved

#16 by R. J. Mathar at Sat Mar 11 14:41:56 EST 2017

CROSSREFS

Cf. A067911, A056916, A055774.

STATUS

approved

editing

#15 by Jon E. Schoenfield at Thu Aug 06 01:34:58 EDT 2015

STATUS

editing

approved

#14 by Jon E. Schoenfield at Thu Aug 06 01:34:55 EDT 2015

NAME

Proda( n) = Product_{k=1..n, } lcm(n,k) ).

COMMENTS

Log(a(n))/n/Log(n) is bounded since n^n < a(n) < n^(2n). It seems that lim n -> infinity Log(a(n))/n/Log(n) exists and = 1.7..... - Benoit Cloitre, Aug 13 2002

MAPLE

A071248 := proc(n) mul( lcm(k, n), k=1..n) ; end: for n from 1 to 10 do printf("%d ", A071248(n)) ; od ; - _# _R. J. Mathar_, Apr 03 2007

STATUS

approved

editing

#13 by N. J. A. Sloane at Thu Dec 05 19:55:20 EST 2013

AUTHOR

_Amarnath Murthy (amarnath_murthy(AT)yahoo.com), _, May 21 2002

Discussion

Thu Dec 05

19:55

OEIS Server: https://oeis.org/edit/global/2075

#12 by Charles R Greathouse IV at Fri May 10 12:45:01 EDT 2013

FORMULA

a(n) = n!*Product_{ d divides n } d^phi(d). - _Vladeta Jovovic (vladeta(AT)eunet.rs), _, Sep 10 2004

Discussion

Fri May 10

12:45

OEIS Server: https://oeis.org/edit/global/1911

#11 by Russ Cox at Fri Mar 30 18:39:00 EDT 2012

COMMENTS

Log(a(n))/n/Log(n) is bounded since n^n < a(n) < n^(2n). It seems that lim n -> infinity Log(a(n))/n/Log(n) exists and = 1.7..... - _Benoit Cloitre (benoit7848c(AT)orange.fr), _, Aug 13 2002

EXTENSIONS

More terms from _Benoit Cloitre (benoit7848c(AT)orange.fr), _, Aug 13 2002

Discussion

Fri Mar 30

18:39

OEIS Server: https://oeis.org/edit/global/216

#10 by Russ Cox at Fri Mar 30 17:38:43 EDT 2012

FORMULA

a(n) = n!*n^n/A067911(n)=A000142(n)*A000312(n)/A067911(n). - _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Apr 03 2007

MAPLE

A071248 := proc(n) mul( lcm(k, n), k=1..n) ; end: for n from 1 to 10 do printf("%d ", A071248(n)) ; od ; - _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Apr 03 2007

Discussion

Fri Mar 30

17:38

OEIS Server: https://oeis.org/edit/global/190