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

3,1

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A006530, A093074.

Sequence in context: A262941 A127656 A109709 * A216685 A331853 A187184

Adjacent sequences: A125601 A125602 A125603 * A125605 A125606 A125607

Keyword

nonn,look

Author

Carlos Alves, Nov 27 2006

Status

approved