A087713 Greatest prime factor of the product of the neighbors of the n-th prime.

3, 2, 3, 3, 5, 7, 3, 5, 11, 7, 5, 19, 7, 11, 23, 13, 29, 31, 17, 7, 37, 13, 41, 11, 7, 17, 17, 53, 11, 19, 7, 13, 23, 23, 37, 19, 79, 41, 83, 43, 89, 13, 19, 97, 11, 11, 53, 37, 113, 23, 29, 17, 11, 7, 43, 131, 67, 17, 139, 47, 71, 73, 17, 31, 157, 79, 83, 13, 173, 29, 59

Offset: 1

Author

Reinhard Zumkeller, Sep 28 2003

Keywords

• nonn
• easy

Comments

Apparently a(n) = A024710(n) for n>4. - Georg Fischer, Oct 06 2018

Conjecture: The record values are A120628 \ {2}. - Jason Yuen, Jan 19 2025

Examples

			a(10) = A006530(prime(10)^2 - 1) = A006530(29*29-1) = A006530(840) = A006530(7*5*3*2^3) = 7.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Davide Rotondo and others, A120628 and record numbers of a087713, Conversation in the SeqFan Google Group, Dec 25 2024.

Crossrefs

Cf. A006530, A084920, A120628.

Programs

Haskell

a087713 = a006530 . a084920  -- Reinhard Zumkeller, Aug 27 2013

Mathematica

FactorInteger[#][[-1,1]]&/@((#-1)(#+1)&/@Prime[Range[80]]) (* Harvey P. Dale, Oct 26 2019 *)

PARI

a(n) = my(p=prime(n)); vecmax(factor((p-1)*(p+1))[, 1]); \\ Michel Marcus, Jan 20 2025

Python

from sympy import prime, primefactors
def A087713(n): p = prime(n); return max(primefactors(p*p-1))  # Ya-Ping Lu, Mar 07 2025

Formula

a(n) = A006530((A000040(n)-1)*(A000040(n)+1)) = A006530(A006093(n)*A008864(n)) = A006530(A084920(n)).

a(n) <= (prime(n)+1)/2, n > 1. - Ya-Ping Lu, Apr 10 2025

Extensions

Definition clarified by Harvey P. Dale, Oct 26 2019