A254278 Numbers that are smaller than the sum of their deficient divisors.

2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 98, 99, 101, 102, 103, 104, 105

Offset

1,1

Comments

Contains every deficient number larger than 1 and every primitive abundant number (A071395).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

a(16) = 20 since 20 is smaller than 22, which is the sum of its deficient divisors.

Mathematica

Select[Range@ 105, Function[n, n < Total@ Select[Divisors@ n, DivisorSigma[1, #] < 2 # &]]] (* Michael De Vlieger, Jul 16 2016 *)

Prog

(PARI) isok(n) = n < sumdiv(n, d, d*(sigma(d) < 2*d)); \\ Michel Marcus, Jun 26 2019

Crossrefs

Cf. A005100, supersequence of A071395 and A198471, A091191.

Sequence in context: A039215 A047253 A248910 * A204878 A037918 A043091

Adjacent sequences: A254275 A254276 A254277 * A254279 A254280 A254281

Keyword

nonn

Author

Timothy L. Tiffin, Jul 15 2016

Status

approved