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A147763
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a(n) = smallest k such that n = d*(d-b)*(d+c), where b, c, d >= 0 and k = b+c.
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0
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0, 1, 2, 1, 4, 2, 6, 0, 2, 4, 10, 1, 12, 6, 4, 2, 16, 1, 18, 3, 6, 10, 22, 2, 4, 12, 0, 5, 28, 3, 30, 2, 10, 16, 6, 1, 36, 18, 12, 3, 40, 5, 42, 9, 2, 22, 46, 1, 6, 3, 16, 11, 52, 3, 10, 5, 18, 28, 58, 2, 60, 30, 4, 0, 12, 9, 66, 15, 22, 5, 70, 3, 72, 36, 2, 17, 10, 11, 78, 1, 6, 40, 82, 4, 16
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n) = n-1 for n prime; a(n) = 0 for n a 3rd power.
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EXAMPLE
| n = 9 = 3*1*3 = 3*(3-2)*(3+0) with d = 3, b = 2, c = 0. So a(9) = k = 2+0 = 2, since there is no solution with k = 1.
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PROG
| (MAGMA) [ Min(v) where v is [ b+c: d, y, z in Divisors(n) | d*(d-b)*(d+c) eq n and d ge 0 and b ge 0 and c ge 0 where b is d-y where c is z-d ]: n in [1..85] ];
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CROSSREFS
| A056737
Sequence in context: A161077 A161293 A057923 * A098371 A070777 A173614
Adjacent sequences: A147760 A147761 A147762 * A147764 A147765 A147766
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KEYWORD
| nonn
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AUTHOR
| Samuel Zbarsky (sa_zbarsky(AT)yahoo.com), Nov 11 2008
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EXTENSIONS
| Edited definition and example. Added comment and MAGMA program. Extended beyond a(42). - Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 19 2008
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