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A075777
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Minimal surface area of a rectangular solid with volume n and integer sides.
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2
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6, 10, 14, 16, 22, 22, 30, 24, 30, 34, 46, 32, 54, 46, 46, 40, 70, 42, 78, 48, 62, 70, 94, 52, 70, 82, 54, 64, 118, 62, 126, 64, 94, 106, 94, 66, 150, 118, 110, 76, 166, 82, 174, 96, 78, 142, 190, 80, 126, 90, 142, 112, 214, 90, 142, 100, 158, 178, 238, 94, 246, 190
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| To find minimum surface area, let s1_0 = [n^(1/3)]. Find largest integer s1 such that s1 <= s1_0 and s1 | n. Then let s2_0 = [sqrt(n / s1)]. Find largest integer s2 such that s2 <= s2_0 and s2 | (n / s1). Then s3 = n / (s1 * s2). And minimum surface area a(n) = 2 * (s1 * s2 + s1 * s3 + s2 * s3).
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EXAMPLE
| a(12) = 32 because side lengths of 2, 2 and 3 will give volume 12 and surface area 32, which is the minimum surface area.
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CROSSREFS
| Cf. A135711.
Sequence in context: A162409 A183072 A193416 * A178246 A190712 A167200
Adjacent sequences: A075774 A075775 A075776 * A075778 A075779 A075780
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KEYWORD
| easy,nonn
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AUTHOR
| Robert A. Stump (bee_ess107(AT)msn.com), Oct 09 2002
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