login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A048671 a(n) is the least common multiple of the proper divisors of n. 12
1, 1, 1, 2, 1, 6, 1, 4, 3, 10, 1, 12, 1, 14, 15, 8, 1, 18, 1, 20, 21, 22, 1, 24, 5, 26, 9, 28, 1, 30, 1, 16, 33, 34, 35, 36, 1, 38, 39, 40, 1, 42, 1, 44, 45, 46, 1, 48, 7, 50, 51, 52, 1, 54, 55, 56, 57, 58, 1, 60, 1, 62, 63, 32, 65, 66, 1, 68, 69, 70, 1, 72, 1, 74, 75, 76, 77, 78, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A proper divisor d of n is a divisor of n such that 1 <= d < n.

Previous name was: a(n) = q(n)/q(n-1), where q(n) = n!/A003418(n).

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Peter Luschny and Stefan Wehmeier, The lcm(1,2,...,n) as a product of sine values sampled over the points in Farey sequences, arXiv:0909.1838 [math.CA], 2009.

Eric Weisstein's World of Mathematics, Sylvester Cyclotomic Number

Index entries for sequences related to lcm's

FORMULA

a(n) = A025527(n)/A025527(n-1) or (n*lcm(1..n-1))/lcm(1..n) = (n*A003418(n-1))/A003418(n).

Also a(n) = A003418(n)/A002944(n) = lcm[1, .., n]/lcm[.., C[n, j], ..].

a(n) = n/A014963(n) = lcm(A052126(n), A032742(n)); a(n) = n if n not a prime power, a(n) = n/p if n = p^m (i.e., a(n) = 1 if n = p). - Henry Bottomley, May 19 2000

a(n) = n*Product_{ d divides n } d^mu(d). Product_{ d divides n } a(d) = A007956(n). - Vladeta Jovovic, Jul 04 2002

a(n) = Product_{k=1..n-1, if(gcd(n, k)>1, 1-exp(2*pi*i*k/n), 1)}, i=sqrt(-1). - Paul Barry, Apr 15 2005

a(n) = Product_{k=1..n-1} (if(gcd(k,n)>1, 2*Pi/Gamma(k/n)^2, 1); a(n) = Product_{k=1..n-1} (if(gcd(k,n)>1, 2*sin(Pi*k/n), 1). - Peter Luschny, Jun 09 2011

EXAMPLE

8!/lcm(8) = 48 = 40320/840 while 7!/lcm(7) = 5040/420 = 12 so a(8) = 48/12 = 4.

a(5) = 1 = lcm(1,2,3,4,5)/lcm(1,5,10,10,5,1).

MAPLE

A048671 := n -> ilcm(op(numtheory[divisors](n) minus {1, n}));

seq(A048671(i), i=1..79); # Peter Luschny, Mar 21 2011

MATHEMATICA

{1}~Join~Table[LCM @@ Most@ Divisors@ n, {n, 2, 79}] (* Michael De Vlieger, May 01 2016 *)

PROG

(PARI) a(n)=my(p=n); if(isprime(n)||(ispower(n, , &p)&&isprime(p)), n/p, n) \\ Charles R Greathouse IV, Jun 24 2011

(PARI) a(n)=my(p); if(isprimepower(n, &p), n/p, n) \\ Charles R Greathouse IV, May 02 2016

(Sage)

def A048671(n) :

    if n < 2 : return 1

    else : D = divisors(n); D.pop()

    return lcm(D)

[A048671(i) for i in (1..79)] # Peter Luschny, Feb 03 2012

CROSSREFS

Cf. A025527, A003418, A002944, A000142, A014963.

Cf. A182936 gives the dual (greatest common divisor).

Sequence in context: A189733 A277791 A243146 * A205959 A318503 A088123

Adjacent sequences:  A048668 A048669 A048670 * A048672 A048673 A048674

KEYWORD

nonn,easy

AUTHOR

Labos Elemer

EXTENSIONS

New definition based on a comment of David Wasserman by Peter Luschny, Mar 23 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 13 15:03 EST 2018. Contains 318086 sequences. (Running on oeis4.)