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Sum of divisors (A000203) of deficient numbers (A005100).
5

%I #10 Jan 02 2015 18:49:41

%S 1,3,4,7,6,8,15,13,18,12,14,24,24,31,18,20,32,36,24,31,42,40,30,32,63,

%T 48,54,48,38,60,56,42,44,84,78,72,48,57,93,72,98,54,72,80,90,60,62,96,

%U 104,127,84,68,126,96,72,74,114,124,140,96,80,121,126,84,108,132

%N Sum of divisors (A000203) of deficient numbers (A005100).

%C a(n) = A000203(A005100(n)) = A005100(n) + A205099(n).

%H Harvey P. Dale, <a href="/A204823/b204823.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DeficientNumber.html">Deficient Number</a>

%F a(n) < 8n/3. - _Charles R Greathouse IV_, Feb 19 2013

%t sddn[n_]:=Module[{s=DivisorSigma[1,n]},If[s<2n,s,0]]; DeleteCases[ sddn/@ Range[ 100],0] (* _Harvey P. Dale_, Jan 02 2015 *)

%o (PARI) for(n=1,300,s=sigma(n);if(s<2*n,print1(s", "))) \\ _Charles R Greathouse IV_, Feb 19 2013

%Y Cf. A204822 (sum of divisors of abundant numbers), A205099 (sum of proper divisors of deficient numbers).

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Jan 22 2012