A091192 Abundant numbers having at least one abundant proper divisor.

24, 36, 40, 48, 54, 60, 72, 80, 84, 90, 96, 100, 108, 112, 120, 126, 132, 140, 144, 150, 156, 160, 162, 168, 176, 180, 192, 198, 200, 204, 208, 210, 216, 220, 224, 228, 234, 240, 252, 260, 264, 270, 276, 280, 288, 294, 300, 306, 312, 320, 324, 330, 336, 340

Offset: 1

Author

Reinhard Zumkeller, Dec 27 2003

Keywords

• nonn

Comments

A080224(a(n))>1.

Examples

			24 is in the sequence since it is abundant, and 12 is a divisor of 24 which is also abundant.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Abundant Number

Crossrefs

Cf. A005101, A080224, A091191.

Programs

Mathematica

aQ[n_] := Module[{d = Divisors[n]}, Total@d > 2 n && AnyTrue[d[[2 ;; -2]], DivisorSigma[1, #] > 2# &]]; Select[Range[340], aQ] (* Amiram Eldar, Jun 21 2019 *)

PARI

isabund(n) = sigma(n) > 2*n;
isok(n) = {if (isabund(n), fordiv(n, d, if ((dMichel Marcus, Jun 21 2019