A236454 Smallest number not dividing n^2.

2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2

Offset: 1

Author

Antti Karttunen, Jan 26 2014

Keywords

• nonn

Comments

Differs from A053669, "smallest prime not dividing n", for the first time at n=210, where a(210)=8, while A053669(210)=11. A235921 lists all n for which a(n) differs from A053669(n).

Differs from A214720 at n=2, 210, 630, 1050, 1470, 1890, 2310,.... - R. J. Mathar, Mar 30 2014

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

One more than A235918.

Cf. A003418, A019554.

Cf. also A000290, A007978, A053669, A235921.

Programs

Maple

A236454 := proc(n)
    for m from 2 do
        if modp(n^2,m) <> 0 then
            return m;
        end if;
    end do:
end proc:# R. J. Mathar, Mar 30 2014

Mathematica

Join[{2,3},Table[Complement[Range[n],Divisors[n^2]][[1]],{n,3,90}]] (* Harvey P. Dale, Mar 18 2018 *)

Scheme

(define (A236454 n) (A007978 (A000290 n)))

Formula

a(n) = A007978(A000290(n)) = A007978(n^2).

a(n) = A235918(n)+1.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=0} 1/A019554(A003418(k)) = 2.91240643793540602415... . - Amiram Eldar, Jan 14 2024