The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A246048 Numbers for which (n^2)! is divisible by n!^n*(2n)!. 2
6, 12, 14, 15, 21, 22, 24, 26, 28, 30, 35, 38, 39, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 69, 70, 74, 75, 76, 77, 78, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
In general, (n*m)! is divisible by m!^n*n!, cf. A060540 for the quotients. It was asked when it is also divisible by m!^n*(kn)! for some k>1. The present sequence answers this for the special case m=n. For the values m=n=52,69,75,77,78,92,95,... one can take k=3; m=n=120 is the least case where one can take k=4.
Farideh Firoozbakht observes that all terms are composite numbers. The comment in A057599 and conjecture in A096126 seem to confirm that there are no primes nor powers of primes in this sequence.
LINKS
PROG
(PARI) max_k(n)=for(k=1, m=n, Mod((n*m)!, m!^n*(k*n)!) && return(k-1)) \\ returns the maximal k for m=n.
for(n=1, 99, a(n)>1&&print1(n, ", ")) \\ prints this sequence
CROSSREFS
Sequence in context: A325700 A360551 A306999 * A348251 A290648 A336549
KEYWORD
nonn
AUTHOR
M. F. Hasler, Aug 23 2014
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 May 29 21:02 EDT 2024. Contains 372952 sequences. (Running on oeis4.)