A198471 Abundant numbers that are smaller than the sum of their deficient divisors.

20, 30, 42, 66, 70, 78, 88, 102, 104, 114, 138, 150, 174, 186, 210, 220, 222, 246, 258, 260, 272, 282, 294, 304, 308, 318, 330, 340, 354, 364, 366, 368, 380, 390, 402, 426, 438, 450, 460, 462, 464, 474, 476, 498, 510, 532, 534, 546, 550, 570, 572, 580, 582, 606

Offset: 1

Author

Timothy L. Tiffin, Jan 07 2013

Keywords

• nonn

Comments

The primitive abundant number sequence (A071395) is a subsequence of this sequence.

Examples

			a(5) = 70 since 70 is smaller than 74, which is the sum of its deficient divisors.
		

Links

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

Crossrefs

Cf. A071395, A198471, A125310.

Programs

Mathematica

totdef[n_] := Total@Select[Divisors@n, DivisorSigma[-1, #] < 2 &]; Select[Range[570], DivisorSigma[-1, #] > 2 && # < totdef[#] &] (* Giovanni Resta, Jan 09 2013 *)

PARI

isok(n) = (sigma(n) > 2*n) && (n < sumdiv(n, d, if (sigma(d) < 2*d, d))); \\ Michel Marcus, Jun 21 2019

Extensions

a(21)-a(50) from Giovanni Resta, Jan 09 2013