A117369 a(n) = smallest prime which is > smallest prime dividing n and is coprime to n.

2, 3, 5, 3, 7, 5, 11, 3, 5, 3, 13, 5, 17, 3, 7, 3, 19, 5, 23, 3, 5, 3, 29, 5, 7, 3, 5, 3, 31, 7, 37, 3, 5, 3, 11, 5, 41, 3, 5, 3, 43, 5, 47, 3, 7, 3, 53, 5, 11, 3, 5, 3, 59, 5, 7, 3, 5, 3, 61, 7, 67, 3, 5, 3, 7, 5, 71, 3, 5, 3, 73, 5, 79, 3, 7

Offset: 1

Author

Leroy Quet, Mar 10 2006

Keywords

• nonn

Examples

			a(6) = 5 because 5 is the smallest prime which is both greater than the smallest prime dividing 6, which is 2 and is coprime to 6.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A079068, A117367.

Programs

Mathematica

a[1] := 2; a[n_] := Module[{}, k = PrimePi[FactorInteger[n][[1, 1]]]; k++; While[Not[GCD[Prime[k], n] == 1 ], k++ ]; Prime[k]]; Table[a[i], {i, 1, 80}] (* Stefan Steinerberger and Patrick Hanslmaier, Jun 03 2007 *)
spdn[n_]:=Module[{s=FactorInteger[n][[1,1]],p},p=NextPrime[s];While[ !CoprimeQ[ p,n],p=NextPrime[p]];p]; Array[spdn,80] (* Harvey P. Dale, Feb 18 2018 *)

Extensions

More terms from Stefan Steinerberger and Patrick Hanslmaier, Jun 03 2007