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

1,1

Comments

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

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A071395, A198471, A125310.

Sequence in context: A109944 A108030 A095787 * A120145 A104048 A078499

Adjacent sequences: A198468 A198469 A198470 * A198472 A198473 A198474

Keyword

nonn

Author

Timothy L. Tiffin, Jan 07 2013

Extensions

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

Status

approved