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

Author

Timothy L. Tiffin, Jul 15 2016

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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