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

1,3

Comments

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A117364, A117366, A117367, A117368.

Sequence in context: A163961 A354366 A101387 * A116212 A079068 A133021

Adjacent sequences: A117362 A117363 A117364 * A117366 A117367 A117368

Keyword

nonn

Author

Leroy Quet, Mar 10 2006

Extensions

More terms from Stefan Steinerberger, Mar 14 2006

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

Status

approved