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Search: id:A117346
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| A117346 |
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Near-multiperfects: numbers n such that abs ( sigma ( n ) mod n ) <= ln ( n ). |
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5
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| 3, 4, 5, 6, 7, 8, 10, 11, 13, 16, 17, 19, 20, 23, 28, 29, 31, 32, 37, 41, 43, 47, 53, 59, 61, 64, 67, 70, 71, 73, 79, 83, 88, 89, 97, 101, 103, 104, 107, 109, 110, 113, 120, 127, 128, 131, 136, 137, 139, 149, 151, 152, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Sequences A117346 through A117350 are an attempt to improve on sequences A045768 through A045770, A077374, A087167, A087485, and A088007 through A088012, and related sequences, ( but not to replace them ), by using a more significant definition of "near" . E.g. is sigma ( n ) really "near" a multiple of n, for n = 9 ? Or n = 18 ? ln is the natural logarithm . sigma is the sum_of_divisors function.
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, B2.
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LINKS
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Eric Weisstein's World of Mathematics, Multiperfect Number
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FORMULA
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sigma ( n ) = k * n + r, abs ( r ) <= ln ( n )
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EXAMPLE
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70 is in the sequence because sigma ( 70 ) = 144 = 2 * 70 + 4,
while 4 < ln ( 70 ) ~= 4.248.
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CROSSREFS
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Cf. A045768 through A045770, A077374, A087167, A087485, A088007 through A088012, A117347 through A117350.
Sequence in context: A026423 A026427 A026482 this_sequence A039078 A073632 A066378
Adjacent sequences: A117343 A117344 A117345 this_sequence A117347 A117348 A117349
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KEYWORD
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nonn
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AUTHOR
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Walter Nissen (wnissen(AT)tfn.net), Mar 09 2006
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