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A080226 Number of deficient divisors of n.

%I A080226 #15 Feb 16 2025 08:32:48
%S A080226 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 A080226 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 A080226 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 A080226 Number of deficient divisors of n.
%C A080226 Number of divisors d of n with sigma(d)<2*d (sigma = A000203).
%H A080226 Antti Karttunen, <a href="/A080226/b080226.txt">Table of n, a(n) for n = 1..20000</a>
%H A080226 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DeficientNumber.html">Deficient Number.</a>
%F A080226 A080224(n) + A080225(n) + a(n) = A000005(n).
%F A080226 a(n) = Sum_{d|n} A294934(d) = A294926(n) + A294934(n). - _Antti Karttunen_, Nov 14 2017
%e A080226 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 A080226 a[n_] := Sum[If[DivisorSigma[1, d] < 2d, 1, 0], {d, Divisors[n]}];
%t A080226 Array[a, 105] (* _Jean-François Alcover_, Dec 02 2021 *)
%o A080226 (PARI) A080226(n) = sumdiv(n, d, (sigma(d)<(2*d))); \\ _Antti Karttunen_, Nov 14 2017
%Y A080226 Cf. A000203, A005100, A187793, A294926, A294934.
%K A080226 nonn
%O A080226 1,2
%A A080226 _Reinhard Zumkeller_, Feb 07 2003