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A082024
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Number of partitions of n into 3 parts which have common divisors.
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1
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0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 4, 0, 4, 3, 5, 0, 9, 0, 9, 5, 10, 0, 16, 2, 14, 7, 17, 0, 27, 0, 21, 11, 24, 6, 36, 0, 30, 15, 37, 0, 51, 0, 41, 25, 44, 0, 64, 4, 58, 25, 57, 0, 81, 12, 69, 31, 70, 0, 108, 0, 80, 43, 85, 16, 123, 0, 97, 45, 120, 0, 144, 0, 114, 69, 121, 14, 171, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,11
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COMMENTS
| a(p) = 0 if p is a prime. Can any one suggest a formula?
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EXAMPLE
| a(14) = 4 and the partitions are (10,2,2), (8,4,2),(6,6,2) and (6,4,4).
a(13) = 0 as for all r + s + t = 13,r > 0, s > 0,t> 0 GCD(r,s,t) = 1.
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MATHEMATICA
| a[n_] := Length[Select[Flatten[Table[{a, b, n-a-b}, {a, 1, Floor[n/3]}, {b, a, Floor[(n-a)/2]}], 1], GCD@@#1>1&]]
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CROSSREFS
| Cf. A082023.
Sequence in context: A046769 A145893 A137561 * A114402 A035647 A065806
Adjacent sequences: A082021 A082022 A082023 * A082025 A082026 A082027
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 07 2003
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EXTENSIONS
| More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 20 2003 and Dean Hickerson (dean.hickerson(AT)yahoo.com), Apr 22 2003
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