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

1,1

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

Links

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

Example

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

Maple

filter:= n -> convert(select(d -> numtheory:-sigma(d) < 2*d, numtheory:-divisors(n)), `+`)<n:
select(filter, [$1..1000]); # 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 *)

Prog

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

Crossrefs

Cf. A125310.

Sequence in context: A055482 A284342 A362844 * A245379 A363814 A224218

Adjacent sequences: A198467 A198468 A198469 * A198471 A198472 A198473

Keyword

nonn

Author

Timothy L. Tiffin, Jan 07 2013

Extensions

More terms from Robert Israel, Dec 28 2017

Status

approved