A094802 a(n) = smallest k such that all of 1 through n divides k!.

1, 2, 3, 4, 5, 5, 7, 7, 7, 7, 11, 11, 13, 13, 13, 13, 17, 17, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 29, 29, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 41, 41, 43, 43, 43, 43, 47, 47, 47, 47, 47, 47, 53, 53, 53, 53, 53, 53, 59, 59

Offset

1,2

Comments

It is conjectured that after n=4 the sequence is prime for n prime or the previous prime for n not prime.

Links

Table of n, a(n) for n=1..60.

Example

a(6)=5 as 5!=120 which is divisible by 1,2,3,4,5 and 6.

Maple

A094802 := proc(n)
    local k, nlcm ;
    nlcm := A003418(n) ;
    for k from 1 do
        if modp(k!, nlcm) = 0 then
            return k ;
        end if;
    end do:
end proc:
seq(A094802(n), n=1..30) ; # R. J. Mathar, Nov 15 2019

Mathematica

a[n_] := Module[{k = 1}, While[True, If[AllTrue[Range[n], Divisible[k!, #]&], Return[k]]; k++]];
Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Apr 01 2024 *)

Prog

(PARI) { for (i=1, 60, x=1; for (j=1, i, xf=x!; if (xf%j!=0, x+=1; j=1)); print1(", "x)) }

Crossrefs

Cf. A002034, A007917.

Sequence in context: A319057 A181894 A265535 * A075084 A086593 A073757

Adjacent sequences: A094799 A094800 A094801 * A094803 A094804 A094805

Keyword

nonn

Author

Jon Perry, Jun 11 2004

Extensions

Corrected by T. D. Noe, Nov 02 2006

Status

approved