A117364 a(n) = largest prime less than the largest prime dividing n (or 1 if there is no such prime).

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

Offset: 1

Author

Leroy Quet, Mar 10 2006

Keywords

• nonn

Comments

a(n) = 1 if and only if n is a power of 2 (including 1).

a(n/3) = 2 iff n/3 is A003586: 3-smooth numbers: numbers of the form 2^i*3^j with i, j >= 0.

a(n/5) = 3 iff n/5 is A051037: 5-smooth numbers: i.e. numbers whose prime divisors are all <= 5, etc.

Examples

			5 is the largest prime dividing 10. So a(10) is the largest prime < 5, which is 3.
		

Crossrefs

Cf. A117365, A117366, A117367.

Programs

Mathematica

PrevPrime[n_] := Block[{k = n - 1}, While[ ! PrimeQ[k], k-- ]; k]; f[n_] := Block[{k = PrevPrime@ FactorInteger[Max[2, n]][[ -1, 1]]}, If[k > 1, k, 1]]; Array[f, 87] (* Robert G. Wilson v *)

Extensions

More terms from Robert G. Wilson v, May 01 2006