A125604 Minimum of the largest prime factors of a number and its two neighbors.

2, 2, 2, 3, 2, 2, 2, 3, 3, 3, 3, 5, 2, 2, 2, 3, 3, 5, 5, 7, 3, 3, 3, 3, 3, 3, 5, 5, 2, 2, 2, 7, 3, 3, 3, 13, 5, 5, 5, 7, 7, 5, 5, 5, 3, 3, 3, 5, 5, 13, 3, 3, 3, 7, 7, 19, 5, 5, 5, 7, 2, 2, 2, 11, 11, 17, 7, 7, 3, 3, 3, 5, 5, 5, 11, 11, 5, 3, 3, 3, 7, 7, 7, 17, 11, 11, 5, 5, 5, 13, 23, 19, 3, 3, 3, 7, 5, 5

Offset: 3

Author

Carlos Alves, Nov 27 2006

Keywords

• nonn
• look

Examples

			a(93) = min{lpf(92),lpf(93),lpf(94)} = min{23,31,47} = 23.
		

Links

• Robert Israel, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A006530, A093074.

Programs

Maple

LPF:= map(t -> max(numtheory:-factorset(t)), [$2..101]):
[seq](min(LPF[i..i+2]),i=1..nops(LPF)-2); # Robert Israel, Jun 16 2025

Mathematica

LPF = FactorInteger[ # ][[ -1, 1]] &; Map[Min[{LPF[ # - 1], LPF[ # ], LPF[ # + 1]}] &, Range[3, 200]]
Min/@Partition[Table[FactorInteger[n][[-1,1]],{n,110}],3,1] (* Harvey P. Dale, May 25 2015 *)

PARI

a(n) = my(lpf(k)=vecmax(factor(k)[, 1])); vecmin([lpf(n-1), lpf(n), lpf(n+1)]); \\ Ruud H.G. van Tol, Aug 15 2024

Python

from sympy import primefactors
def a(n): return min(map(lambda n: primefactors(n)[-1], range(n-1,n+2))) # David Radcliffe, Jun 16 2025

Formula

a(n) = min{lpf(n-1),lpf(n),lpf(n+1)}, where lpf is the largest prime factor: lpf(k) = A006530(k).