login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A048671 a(n) is the least common multiple of the proper divisors of n. 16
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
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.
FORMULA
a(n) = A025527(n)/A025527(n-1).
a(n) = (n*A003418(n-1))/A003418(n).
a(n) = A003418(n-1)/A002944(n). [corrected by Michel Marcus, May 18 2020]
From Henry Bottomley, May 19 2000: (Start)
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). (End)
From Vladeta Jovovic, Jul 04 2002: (Start)
a(n) = n*Product_{d | n} d^mu(d).
Product_{d | n} a(d) = A007956(n). (End)
a(n) = Product_{k=1..n-1} if(gcd(n, k) > 1, 1 - exp(2*pi*i*k/n), 1), where i = sqrt(-1). - Paul Barry, Apr 15 2005
From Peter Luschny, Jun 09 2011: (Start)
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). (End)
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. A182936 gives the dual (greatest common divisor).
Sequence in context: A277791 A243146 A349440 * A335023 A205959 A318503
KEYWORD
nonn,easy
AUTHOR
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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)