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Search: id:A071927
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| A071927 |
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Barely abundant numbers: abundant n such that sigma(n)/n < sigma(m)/m for all abundant numbers m<n, sigma(n) being the sum of the divisors of n. |
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| 12, 18, 20, 70, 88, 104, 464, 650, 1888, 1952, 4030, 5830, 8925, 17816, 26742, 26778, 26886, 26898, 26958, 27042, 27078, 27102, 27114, 27138, 27282, 27294, 27366, 27402, 27498, 27546, 27582, 27618, 27726, 27822, 27834, 27858, 27894, 27906
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The 103 prime numbers in the range 4457 to 5351, multiplied by 6, produce 103 terms of the series and likewise for the 33774 primes in the range 924493 through 1396393. There are likely to be similar long runs of a range of prime numbers multiplied by 6 further in the sequence. One could eliminate these by adding the requirement that n be primitive abundant, whose only additional effect would be to eliminate the first two terms of the sequence.
The inverse of this series, barely deficient numbers, includes all powers of 2 since their proper divisors always add up to one less than themselves. No other number through 2^24 has this attribute.
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MATHEMATICA
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r = 3; Do[ s = DivisorSigma[1, n]/n; If[ s > 2 && s < r, Print[n]; r = s], {n, 1, 32200}]
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CROSSREFS
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Cf. A004394.
Sequence in context: A098899 A098770 A091191 this_sequence A031207 A107794 A162151
Adjacent sequences: A071924 A071925 A071926 this_sequence A071928 A071929 A071930
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KEYWORD
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nonn
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AUTHOR
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Joe McCauley (mccauley(AT)davesworld.net), Jun 14 2002
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EXTENSIONS
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The sequence begins 12, 18, 20, 70, 88, 104, 464, 650, 1888, 1952, 4030, 5830, 8925, 17816, 26742, [101 terms omitted], 32106, 32128, 77744, 91388, 128768, 130304, 442365, 521728, 522752, 1848964, 5546958, [33772 terms omitted], 8378358, 8378368, 8382464 ...
More terms and Mathematica program from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 18 2002
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