A198470 - OEIS

%I #29 May 09 2021 13:33:07

%S 12,18,24,36,40,48,54,56,60,72,80,84,96,100,108,112,120,126,132,140,

%T 144,156,160,162,168,176,180,192,196,198,200,204,208,216,224,228,234,

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

%C This sequence is a subsequence of the abundant numbers A005101.

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

%H Robert Israel, <a href="/A198470/b198470.txt">Table of n, a(n) for n = 1..10000</a>

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

%p filter:= n -> convert(select(d -> numtheory:-sigma(d) < 2*d, numtheory:-divisors(n)),`+`)<n:

%p select(filter, [$1..1000]); # _Robert Israel_, Dec 28 2017

%t totdef[n_] := Total@Select[Divisors@n, DivisorSigma[-1, #] < 2 &];

%t Select[Range[300], DivisorSigma[-1, #] > 2 && # > totdef[#] &] (* _Giovanni Resta_, Jan 09 2013 *)

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

%Y Cf. A125310.

%K nonn

%O 1,1

%A _Timothy L. Tiffin_, Jan 07 2013

%E More terms from _Robert Israel_, Dec 28 2017