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A126865
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a(n) = GCD(product{p|n}(p+1)^b(p,n), product{p|n}(p-1)^b(p,n)), where the products are over the distinct primes, p, that divide n and p^b(p,n) is the highest power of p dividing n.
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0
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1, 1, 2, 1, 2, 2, 2, 1, 4, 2, 2, 2, 2, 6, 8, 1, 2, 4, 2, 2, 4, 2, 2, 2, 4, 6, 8, 6, 2, 8, 2, 1, 4, 2, 24, 4, 2, 6, 8, 2, 2, 12, 2, 2, 16, 2, 2, 2, 4, 4, 8, 6, 2, 8, 8, 6, 4, 2, 2, 8, 2, 6, 8, 1, 12, 4, 2, 2, 4, 24, 2, 4, 2, 6, 16, 18, 12, 24, 2, 2, 16, 2, 2, 12, 4, 6, 8, 2, 2, 16, 8, 2, 4, 2, 24, 2, 2, 12, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| First occurrence of k or 0 if not possible (including all odd primes k): 2, 1, 0, 9, 0, 14, 0, 15, 0, 0, 0, 42, 0, 0, 0, 45, 0, 76, 0, 589, 0, 0, 0, 35, 0, 0, 0, 4381, 0, 0, ..., . - Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 08 2007
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EXAMPLE
| 400 = 2^4 * 5^2. So a(400) = GCD((2+1)^4 (5+1)^2, (2-1)^4 (5-1)^2) = GCD(2916, 16) = 4.
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MATHEMATICA
| f[n_] := Block[{fi = FactorInteger@n}, GCD[Times @@ ((First /@ fi - 1)^Last /@ fi), Times @@ ((First /@ fi + 1)^Last /@ fi)]]; Array[f, 99] - Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 08 2007
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CROSSREFS
| Cf. A003958, A003959.
Sequence in context: A023645 A167865 A054571 * A104640 A193335 A016727
Adjacent sequences: A126862 A126863 A126864 * A126866 A126867 A126868
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet, Mar 15 2007
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 08 2007
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