A245486 Product of the greatest prime factor of n and the greatest prime factor of n+1.

2, 6, 6, 10, 15, 21, 14, 6, 15, 55, 33, 39, 91, 35, 10, 34, 51, 57, 95, 35, 77, 253, 69, 15, 65, 39, 21, 203, 145, 155, 62, 22, 187, 119, 21, 111, 703, 247, 65, 205, 287, 301, 473, 55, 115, 1081, 141, 21, 35, 85, 221, 689, 159, 33, 77, 133, 551, 1711, 295, 305

Offset: 1

Author

Franklin T. Adams-Watters, Jul 23 2014

Keywords

• nonn
• nice

Comments

We take gpf(1) = 1 by convention.

Except for the initial 2, every member is in A006881.

2^n+1 is never divisible by 23, and when 2^n-1 is divisible by 23, it's also divisible by 89. So 46 cannot occur in the sequence. - Jack Brennen, Jul 23 2014

More generally, let m = A014664(i), i >= 2. If m is odd, 2*A000040(i) occurs in the sequence iff A000040(i) = A006530(2^m-1), in which case it is a(2^m-1). If m is even, 2*A000040(i) occurs in the sequence iff A000040(i) = A006530(2^(m/2)+1), in which case it is a(2^m). - Robert Israel, Jul 24 2014

If a(n) = prime(i)*prime(j), where i < j, then n <= A002072(j). Using this, it can be shown that 3*89 does not occur in the sequence. - Robert Israel, Jul 24 2014

This sequence has an infinite limit; equivalently, each value in A006881 occurs only finitely many times in it. See A002072 for references.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A006530, A006881, A002072, A014664.

Programs

Maple

gpf:= n -> max(numtheory:-factorset(n)):
gpf(1):= 1:
seq(gpf(n)*gpf(n+1),n=1..100); # Robert Israel, Jul 24 2014

Mathematica

gpf[n_] := FactorInteger[n][[-1, 1]]; f[n_] := gpf[n] gpf[n + 1]; Array[f, 60] (* Robert G. Wilson v, Jul 23 2014 *)
Times@@@Partition[Table[FactorInteger[n][[-1,1]],{n,100}],2,1] (* Harvey P. Dale, Sep 24 2017 *)

PARI

gpf(n)=my(ps);if(n<=1,n,ps=factor(n)[,1]~;ps[#ps])
a(n) = gpf(n)*gpf(n+1)

Formula

a(n) = A006530(n) * A006530(n+1).