A117364 - OEIS

%I #9 Apr 09 2014 10:13:41

%S 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,

%T 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,

%U 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

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

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

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

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

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

%t 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_ *)

%Y Cf. A117365, A117366, A117367.

%K nonn

%O 1,3

%A _Leroy Quet_, Mar 10 2006

%E More terms from _Robert G. Wilson v_, May 01 2006