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

%I A198470 #29 May 09 2021 13:33:07
%S A198470 12,18,24,36,40,48,54,56,60,72,80,84,96,100,108,112,120,126,132,140,
%T A198470 144,156,160,162,168,176,180,192,196,198,200,204,208,216,224,228,234,
%U A198470 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
%N A198470 Numbers that are larger than the sum of their deficient divisors.
%C A198470 This sequence is a subsequence of the abundant numbers A005101.
%C A198470 Includes 2^m*p if p is an odd prime and m >= ceiling(log_2(p+1))-1. - _Robert Israel_, Dec 28 2017
%H A198470 Robert Israel, <a href="/A198470/b198470.txt">Table of n, a(n) for n = 1..10000</a>
%e A198470 a(4) = 36 since 36 is larger than 19, which is the sum of its deficient divisors.
%p A198470 filter:= n -> convert(select(d -> numtheory:-sigma(d) < 2*d, numtheory:-divisors(n)),`+`)<n:
%p A198470 select(filter, [$1..1000]); # _Robert Israel_, Dec 28 2017
%t A198470 totdef[n_] := Total@Select[Divisors@n, DivisorSigma[-1, #] < 2 &];
%t A198470 Select[Range[300], DivisorSigma[-1, #] > 2 && # > totdef[#] &] (* _Giovanni Resta_, Jan 09 2013 *)
%o A198470 (PARI) is_A198470(n)=!fordiv(n,d,sigma(d)<2*d & (n-=d)<=0 & return)  \\ _M. F. Hasler_, Jan 11 2013
%Y A198470 Cf. A125310.
%K A198470 nonn
%O A198470 1,1
%A A198470 _Timothy L. Tiffin_, Jan 07 2013
%E A198470 More terms from _Robert Israel_, Dec 28 2017