A245689 Smallest divisor of n that is greater than the smallest prime not dividing n (A053669(n)).

3, 4, 5, 6, 7, 4, 3, 5, 11, 6, 13, 7, 3, 4, 17, 6, 19, 4, 3, 11, 23, 6, 5, 13, 3, 4, 29, 10, 31, 4, 3, 17, 5, 6, 37, 19, 3, 4, 41, 6, 43, 4, 3, 23, 47, 6, 7, 5, 3, 4, 53, 6, 5, 4, 3, 29, 59, 10, 61, 31, 3, 4, 5, 6, 67, 4, 3, 5, 71, 6, 73, 37, 3, 4, 7, 6, 79

Offset: 3

Author

K. Spage, Jul 29 2014

Keywords

• nonn

Comments

Sequence is similar to A126800 but differs for the first time at n = 30 and thereafter at n = 30k, where k = 3, 5, 7, 9, 11, 13, 14, 15 ... The generating function for k is not known.

The sequence starts at n = 3 as there are no qualifying divisors for n = 1 or n = 2.

Examples

			For n = 30 the smallest prime not dividing n is 7 and the smallest divisor of 30 that is greater than 7 is 10, so a(30) = 10.
		

Links

• K. Spage, Table of n, a(n) for n = 3..1000

Crossrefs

Cf. A053669, A245690.

Programs

Maple

a:= proc(n)
uses numtheory;
local F,p;
if n::odd then p:= 2
  else
  F:= map(pi,factorset(n));
  p:= ithprime(min(map(`+`,F,1) minus F));
fi;
min(select(`>`,divisors(n),p));
end proc:
seq(a(n),n=3..100); # Robert Israel, Jul 31 2014

Mathematica

A053669[n_] := Module[{p}, For[p = 2, True, p = NextPrime[p], If[CoprimeQ[n, p], Return[p]]]];
A245689[n_] := SelectFirst[Divisors[n], # > A053669[n]&];
Table[A245689[n], {n, 3, 100}] (* Jean-François Alcover, May 15 2023 *)

PARI

A053669(n)={forprime(p=2, ,if(n%p, return(p)))}
A245689(n) ={my(c=A053669(n)+1);while(n%c,c++);c}

Formula

a(n) = n if n is an odd prime.