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A198470 Numbers that are larger than the sum of their deficient divisors. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is a subset 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: A113756 A055482 A284342 * A245379 A224218 A076485

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

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Last modified January 21 04:53 EST 2020. Contains 331104 sequences. (Running on oeis4.)