A117365 a(n) = largest prime less than the smallest prime dividing n (or 1 if there is no such prime).

1, 1, 2, 1, 3, 1, 5, 1, 2, 1, 7, 1, 11, 1, 2, 1, 13, 1, 17, 1, 2, 1, 19, 1, 3, 1, 2, 1, 23, 1, 29, 1, 2, 1, 3, 1, 31, 1, 2, 1, 37, 1, 41, 1, 2, 1, 43, 1, 5, 1, 2, 1, 47, 1, 3, 1, 2, 1, 53, 1, 59, 1, 2, 1, 3, 1, 61, 1, 2, 1, 67, 1, 71, 1, 2, 1, 5, 1, 73, 1, 2, 1, 79, 1, 3, 1, 2, 1, 83, 1, 5, 1, 2, 1, 3, 1

Offset: 1

Author

Leroy Quet, Mar 10 2006

Keywords

• nonn

Comments

a(n) = 1 if and only if n is even or if n = 1.

Examples

			5 is the smallest prime dividing 35. So a(35) is the largest prime < 5, which is 3.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A117364, A117366, A117367, A117368.

Programs

Mathematica

a[n_] := If[EvenQ[n], 1, Prime[PrimePi[FactorInteger[n][[1]][[1]]] - 1]]; Table[a[n], {n, 2, 80}] (* Stefan Steinerberger, Mar 14 2006 *)
Table[NextPrime[FactorInteger[n][[1, 1]], -1] /. -2 -> 1, {n, 96}] (* Michael De Vlieger, Sep 16 2017 *)

Extensions

More terms from Stefan Steinerberger, Mar 14 2006

More terms from Franklin T. Adams-Watters, Aug 29 2006