cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A073840 Product of the composite numbers between n and 2n (both inclusive).

Original entry on oeis.org

1, 4, 24, 192, 4320, 51840, 120960, 29030400, 65318400, 145152000, 6706022400, 160944537600, 8717829120000, 6590678814720000, 14122883174400000, 30128817438720000, 2112783322890240000, 2662106986841702400000
Offset: 1

Views

Author

Amarnath Murthy, Aug 13 2002

Keywords

Comments

a(n) is divisible by central binomial coefficients, A001405[n]

Examples

			a(6) = 6*8*9*10*12 = 51840.
		

Crossrefs

Programs

  • Maple
    for n from 1 to 50 do l := 1:for j from n to 2*n do if not isprime(j) then l := l*j:fi:od:a[n] := l:od:seq(a[j],j=1..50);
  • Mathematica
    cs[x_] := Flatten[Position[Table[PrimeQ[j], {j, x, 2*x}], False]]+x-1; prcs[x_] := Apply[Times, cs[x]]; Table[prcs[w], {w, 1, 25}]
  • PARI
    a(n)=prod(i=n,2*n,i^if(isprime(i),0,1))

Formula

a(n)=A049614(2n)/A049614(n-1)

Extensions

More terms from Sascha Kurz and Labos Elemer, Aug 14 2002

A073841 LCM of the composite numbers between n and 2n (both inclusive).

Original entry on oeis.org

1, 4, 12, 24, 360, 360, 2520, 5040, 5040, 5040, 55440, 55440, 3603600, 10810800, 10810800, 21621600, 367567200, 367567200, 6983776800, 6983776800, 6983776800, 6983776800, 160626866400, 160626866400, 1124388064800, 1124388064800, 1124388064800, 1124388064800
Offset: 1

Views

Author

Amarnath Murthy, Aug 13 2002

Keywords

Comments

Also, smallest number divisible by all integers 1 through n as well as all composite numbers 1 through 2n. - J. Lowell, Jul 16 2008 [Definition of A140813, that is a duplicate of this sequence]
Not a subsequence of A002182: a(79) = 10703173554082014360835514860858032000 is the smallest term that is not in A002182. [Klaus Brockhaus, Aug 28 2008]

Examples

			a(6) = lcm(6,8,9,10,12) = 360.
The primes <= 10 are 2, 3, 5 and 7. Their highest powers below 2 * 10 = 20 are 16, 9, 5 and 7 respectively. Therefore, a(10) = 16 * 9 * 5 * 7 = 5040. - _David A. Corneth_, Mar 19 2018
		

Crossrefs

Programs

  • Maple
    for n from 1 to 100 do l := 1:for j from n to 2*n do if not isprime(j) then l := lcm(l,j):fi:od:a[n] := l:od: seq(a[j],j=1..100);
  • Mathematica
    Table[ Apply[ LCM, Select[Range[n, 2n], !PrimeQ[ # ] & ]], {n, 2, 26}]
  • PARI
    iscomposite(x) = (x!=1) && !isprime(x);
    a(n) = lcm(select(x->iscomposite(x), vector(n+1, k, n+k-1))); \\ Michel Marcus, Mar 18 2018
    
  • PARI
    a(n) = my(res = 1); forprime(p = 2, n, res *= p^(logint(n<<1, p))); res \\ David A. Corneth, Mar 19 2018

Extensions

Edited by Robert G. Wilson v, Sascha Kurz and Labos Elemer, Aug 14 2002
a(1) changed to 1 by Alois P. Heinz, Mar 18 2018
Showing 1-2 of 2 results.