A242560 Least number k such that (n!-k)/(n-k) is an integer.

2, 1, 2, 2, 4, 3, 6, 4, 6, 5, 10, 6, 12, 7, 10, 8, 16, 9, 18, 10, 14, 11, 22, 12, 24, 13, 18, 14, 28, 15, 30, 16, 22, 17, 28, 18, 36, 19, 26, 20, 40, 21, 42, 22, 30, 23, 46, 24, 42, 25, 34, 26, 52, 27, 44, 28, 38, 29, 58, 30, 60, 31, 42, 32, 52, 33, 66, 34, 46, 35

Offset

1,1

Comments

It is conjectured that a(2n) = n.

The largest k such that (n!-k)/(n-k) is an integer is n!

a(2n+1) <= 2n for all n >= 1.

Does a(n) = A060681(n) for n>1? - Michel Marcus, Oct 24 2015

Links

Table of n, a(n) for n=1..70.

Example

6-1 is not divisible by 6!-1, 6-2 is not divisible by 6!-2, but 6-3 is divisible by 6!-3. So a(6) = 3.

Prog

(PARI) a(n)=for(k=1, n!, if(k!=n, s = (n!-k)/(n-k); if(floor(s)==s, return(k)); ));
n=1; while(n<100, print(a(n)); n+=1) \\ corrected by Michel Marcus, Oct 24 2015

Crossrefs

Sequence in context: A328678 A184199 A262346 * A204596 A324387 A163373

Adjacent sequences: A242557 A242558 A242559 * A242561 A242562 A242563

Keyword

nonn

Author

Derek Orr, May 21 2014

Status

approved