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A245486
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Product of the greatest prime factor of n and the greatest prime factor of n+1.
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3
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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
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OFFSET
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1,1
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COMMENTS
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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
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.
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LINKS
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FORMULA
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MAPLE
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gpf:= n -> max(numtheory:-factorset(n)):
gpf(1):= 1:
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MATHEMATICA
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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 *)
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PROG
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(PARI) gpf(n)=my(ps); if(n<=1, n, ps=factor(n)[, 1]~; ps[#ps])
a(n) = gpf(n)*gpf(n+1)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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