A198470 Numbers that are larger than the sum of their deficient divisors.

12, 18, 24, 36, 40, 48, 54, 56, 60, 72, 80, 84, 96, 100, 108, 112, 120, 126, 132, 140, 144, 156, 160, 162, 168, 176, 180, 192, 196, 198, 200, 204, 208, 216, 224, 228, 234, 240, 252, 264, 270, 276, 280, 288, 300, 306, 312, 320, 324, 336, 342, 348, 350, 352, 360, 372, 378, 384, 392, 396, 400, 408, 414

Offset: 1

Author

Timothy L. Tiffin, Jan 07 2013

Keywords

• nonn

Comments

This sequence is a subsequence of the abundant numbers A005101.

Includes 2^m*p if p is an odd prime and m >= ceiling(log_2(p+1))-1. - Robert Israel, Dec 28 2017

Examples

			a(4) = 36 since 36 is larger than 19, which is the sum of its deficient divisors.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A125310.

Programs

Maple

filter:= n -> convert(select(d -> numtheory:-sigma(d) < 2*d, numtheory:-divisors(n)),`+`)Robert Israel, Dec 28 2017

Mathematica

totdef[n_] := Total@Select[Divisors@n, DivisorSigma[-1, #] < 2 &];
Select[Range[300], DivisorSigma[-1, #] > 2 && # > totdef[#] &] (* Giovanni Resta, Jan 09 2013 *)

PARI

is_A198470(n)=!fordiv(n,d,sigma(d)<2*d & (n-=d)<=0 & return)  \\ M. F. Hasler, Jan 11 2013

Extensions

More terms from Robert Israel, Dec 28 2017