A071927 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.

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

Offset

1,1

Comments

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 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.

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, ...

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A004394.

Sequence in context: A357696 A259980 A257719 * A362052 A247625 A171674

Adjacent sequences: A071924 A071925 A071926 * A071928 A071929 A071930

Keyword

nonn

Author

Joe McCauley (mccauley(AT)davesworld.net), Jun 14 2002

Extensions

More terms from Robert G. Wilson v, Jun 18 2002

Status

approved