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%I #14 Dec 02 2021 06:56:01
%S 1,2,2,3,2,3,2,4,3,4,2,4,2,4,4,5,2,4,2,5,4,4,2,5,3,4,4,5,2,6,2,6,4,4,
%T 4,5,2,4,4,6,2,6,2,6,6,4,2,6,3,6,4,6,2,5,4,6,4,4,2,7,2,4,6,7,4,6,2,6,
%U 4,7,2,6,2,4,6,6,4,6,2,7,5,4,2,7,4,4,4,7,2,8,4,6,4,4,4,7,2,6,6,7,2,6,2,7,8
%N Number of deficient divisors of n.
%C Number of divisors d of n with sigma(d)<2*d (sigma = A000203).
%H Antti Karttunen, <a href="/A080226/b080226.txt">Table of n, a(n) for n = 1..20000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DeficientNumber.html">Deficient Number.</a>
%F A080224(n) + A080225(n) + a(n) = A000005(n).
%F a(n) = Sum_{d|n} A294934(d) = A294926(n) + A294934(n). - _Antti Karttunen_, Nov 14 2017
%e All 4 divisors of n=21 are deficient: 1=A005100(1), 3=A005100(3), 7=A005100(6) and 21=A005100(17), therefore a(21)=4.
%t a[n_] := Sum[If[DivisorSigma[1, d] < 2d, 1, 0], {d, Divisors[n]}];
%t Array[a, 105] (* _Jean-François Alcover_, Dec 02 2021 *)
%o (PARI) A080226(n) = sumdiv(n, d, (sigma(d)<(2*d))); \\ _Antti Karttunen_, Nov 14 2017
%Y Cf. A000203, A005100, A187793, A294926, A294934.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Feb 07 2003
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