A274849 Isolated deficient numbers.

19, 29, 41, 55, 71, 79, 89, 101, 103, 113, 139, 161, 175, 197, 199, 209, 221, 223, 259, 271, 281, 305, 307, 319, 341, 349, 351, 353, 365, 367, 379, 391, 401, 415, 439, 449, 461, 463, 475, 491, 497, 499, 521, 533, 545, 551, 559, 571, 581, 607, 617, 619, 641, 643, 649, 679, 701, 703, 727, 737, 739, 749

Offset

1,1

Comments

Deficient numbers a(n) for which a(n)-1 and a(n)+1 are not deficient. In most instances, both a(n)-1 and a(n)+1 will be abundant numbers; in a few instances, one will be abundant while the other one is perfect.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000 (First 413 terms from Timothy L. Tiffin)

Example

19 is between two abundant numbers (18 and 20), while 29 is between a perfect number (28) and an abundant number (30).

Mathematica

Select[Range@ 750, Boole@ Map[DivisorSigma[1, #] < 2 # &, # + {-1, 0, 1}] == {0, 1, 0} &] (* Michael De Vlieger, Aug 26 2016 *)
SequencePosition[Table[If[DivisorSigma[1, n]<2n, 1, 0], {n, 800}], {0, 1, 0}][[All, 1]]+1 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 21 2017 *)

Crossrefs

Subsequence of A005100.

Sequence in context: A158846 A157026 A240724 * A276049 A108183 A157483

Adjacent sequences: A274846 A274847 A274848 * A274850 A274851 A274852

Keyword

nonn

Author

Timothy L. Tiffin, Jul 08 2016

Status

approved