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Search: id:A117350
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| A117350 |
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Near-multiperfects with primes, powers of 2, 6 * prime and 2^n * prime excluded, abs ( sigma ( n ) mod n ) <= ln ( n ). |
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5
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| 70, 110, 120, 650, 672, 884, 1155, 4030, 5830, 8925, 11096, 17816, 18632, 18904, 30240, 32445, 32760, 45356, 70564, 77744, 85936, 91388, 100804, 116624, 244036, 254012, 388076, 391612, 430272, 442365, 523776, 1090912, 1848964, 2178540
(list; graph; listen)
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OFFSET
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0,1
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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.
The 2-perfect numbers are excluded because they are 2^n * prime.
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CROSSREFS
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Cf. A045768 through A045770, A077374, A087167, A087485, A088007 through A088012, A117346 through A117349.
Sequence in context: A043222 A039399 A044002 this_sequence A004239 A039542 A024748
Adjacent sequences: A117347 A117348 A117349 this_sequence A117351 A117352 A117353
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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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