A061768 k is the least number such that k! is divisible by (k+1)^n.

5, 11, 11, 11, 23, 23, 35, 39, 44, 47, 59, 59, 59, 71, 71, 71, 79, 79, 89, 89, 119, 119, 119, 119, 119, 119, 119, 143, 143, 143, 143, 143, 143, 143, 179, 179, 179, 179, 179, 179, 179, 179, 179, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239, 239

Offset: 1

Author

Robert G. Wilson v, Jun 21 2001

Keywords

• nonn

Examples

			a(4) = 11 as (11 + 1) = 2^2 * 3 and 11! = 2^8 * 3^4 * k (we don't care about the other factors as 12 doesn't divide them). 4 is the largest m such that 12^m divides 11! so a(1) through a(4) are at most 11. - _David A. Corneth_, Mar 15 2019
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• David A. Corneth, PARI program

Programs

Mathematica

Do[k = 1; While[ !IntegerQ[ k! / (k + 1)^n], k++ ]; Print[k], {n, 1, 100} ]

PARI

a(n)=my(k=n);while(k++!%(k+1)^n,);k \\ Charles R Greathouse IV, Apr 16 2015

PARI

See Corneth link \\ David A. Corneth, Mar 15 2019