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A126795
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a(n) = GCD(n, product{p|n}(p+1)), where the product is over the distinct primes, p, that divide n.
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1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 12, 1, 2, 3, 1, 1, 6, 1, 2, 1, 2, 1, 12, 1, 2, 1, 4, 1, 6, 1, 1, 3, 2, 1, 12, 1, 2, 1, 2, 1, 6, 1, 4, 3, 2, 1, 12, 1, 2, 3, 2, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 1, 1, 1, 6, 1, 2, 3, 2, 1, 12, 1, 2, 3, 4, 1, 6, 1, 2, 1, 2, 1, 12, 1, 2, 3, 4, 1, 18, 7, 4, 1, 2, 5, 12, 1, 2, 3, 2, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| a(n) = GCD(n,A048250(n)).
First occurrence of k: 1, 10, 15, 28, 95, 6, 91, 56, 153, 190, 473, 12, 1339, 182, 285, 496, 1139, 90, 703, 380, ..., . - Robert G. Wilson v.
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EXAMPLE
| The distinct primes that divide 28 are 2 and 7. So a(28) = GCD(28, (2+1)(7+1)) = GCD(28, 24) = 4.
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MAPLE
| with(numtheory): a:=proc(n) local fs: fs:=factorset(n): gcd(n, product(1+fs[i], i=1..nops(fs))) end: seq(a(n), n=1..120); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 27 2007
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MATHEMATICA
| f[n_] := GCD[n, Times @@ (First /@ FactorInteger[n] + 1)]; Array[f, 101] (* Robert G. Wilson v *)
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CROSSREFS
| Cf. A048250.
Sequence in context: A040037 A009194 A007732 * A064793 A034460 A063919
Adjacent sequences: A126792 A126793 A126794 * A126796 A126797 A126798
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Mar 14 2007
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 27 2007
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