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Search: id:A125225
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| A125225 |
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Numbers n such that n-1 can be represented as a sum of a subset of divisors of n. |
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1
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| 1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, 60, 64, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 104, 108, 112, 120, 126, 128, 132, 140, 144, 150, 156, 160, 162, 168, 176, 180, 192, 196, 198, 200, 204, 208, 210, 216, 220, 224, 228, 234, 240, 252
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The definition is related to that for semiperfect numbers (A005835). Every practical number (A005153) belongs to this sequence but not necessarily vice versa; e.g., 70 is in this sequence but not practical. Every number n in this sequence has sigma(n) >= 2n-1 (A103288) but, despite being abundant, 102 is not in this sequence.
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REFERENCES
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Such numbers can be used to construct inheritance puzzles of the type described by Premchand Anne (1998). "Egyptian fractions and the inheritance problem". The College Mathematics Journal 29 (4): 296-300.
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EXAMPLE
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70 is in this sequence because 70-1=69=35+14+10+7+2+1 and all numbers in the sum are divisors of 70.
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CROSSREFS
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Cf. A005835, A000225, A005153, A103288.
Adjacent sequences: A125222 A125223 A125224 this_sequence A125226 A125227 A125228
Sequence in context: A058825 A087086 A103288 this_sequence A092903 A005153 A068563
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KEYWORD
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nonn
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AUTHOR
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David Eppstein (eppstein(AT)ics.uci.edu), Jan 13 2007
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