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%I #18 Mar 05 2018 06:31:30
%S 12,18,20,70,88,104,464,650,1888,1952,4030,5830,8925,17816,26742,
%T 26778,26886,26898,26958,27042,27078,27102,27114,27138,27282,27294,
%U 27366,27402,27498,27546,27582,27618,27726,27822,27834,27858,27894,27906
%N 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.
%C 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.
%C The inverse of this sequence, 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.
%C 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, ...
%H T. D. Noe, <a href="/A071927/b071927.txt">Table of n, a(n) for n = 1..1000</a>
%t r = 3; Do[ s = DivisorSigma[1, n]/n; If[ s > 2 && s < r, Print[n]; r = s], {n, 1, 32200}] (* _Robert G. Wilson v_, Jun 18 2002 *)
%o (PARI) lista(nn) = {abk = 3; for (n = 1, nn, ab = sigma(n)/n; if ((ab > 2) && (ab < abk), print1(n, ", "); abk = ab););} \\ _Michel Marcus_, Jun 23 2015
%Y Cf. A004394.
%K nonn
%O 1,1
%A Joe McCauley (mccauley(AT)davesworld.net), Jun 14 2002
%E More terms from _Robert G. Wilson v_, Jun 18 2002
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