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

1,3

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.

Links

Table of n, a(n) for n=1..87.

Example

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

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 *)

Crossrefs

Cf. A117365, A117366, A117367.

Sequence in context: A024467 A215489 A182167 * A193615 A300383 A120250

Adjacent sequences: A117361 A117362 A117363 * A117365 A117366 A117367

Keyword

nonn

Author

Leroy Quet, Mar 10 2006

Extensions

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

Status

approved