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A245486 Product of the greatest prime factor of n and the greatest prime factor of n+1. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
FORMULA
a(n) = A006530(n) * A006530(n+1).
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 *)
PROG
(PARI) gpf(n)=my(ps); if(n<=1, n, ps=factor(n)[, 1]~; ps[#ps])
a(n) = gpf(n)*gpf(n+1)
CROSSREFS
Sequence in context: A063210 A114718 A102261 * A147298 A078636 A083482
KEYWORD
nonn,nice
AUTHOR
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)