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A294888 Sum of nonabundant proper divisors of n.

%I A294888 #11 Nov 17 2017 20:31:00
%S A294888 0,1,1,3,1,6,1,7,4,8,1,16,1,10,9,15,1,21,1,22,11,14,1,24,6,16,13,28,1,
%T A294888 42,1,31,15,20,13,25,1,22,17,30,1,54,1,40,33,26,1,40,8,43,21,46,1,48,
%U A294888 17,64,23,32,1,46,1,34,41,63,19,78,1,58,27,74,1,33,1,40,49,64,19,90,1,46,40,44,1,86,23,46,33,92,1,96,21
%N A294888 Sum of nonabundant proper divisors of n.
%C A294888 Sum of divisors of n smaller than n that are nonabundant numbers (in A263837).
%H A294888 Antti Karttunen, <a href="/A294888/b294888.txt">Table of n, a(n) for n = 1..20000</a>
%H A294888 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%F A294888 a(n) = Sum_{d|n, d<n} A294935(d)*d.
%F A294888 a(n) + A294889(n) = A001065(n).
%e A294888 Proper divisors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45. Of these 1, 2, 3, 5, 6, 9, 10, 15 and 45 are in A263837, thus a(90) = 1+2+3+5+6+9+10+15+45 = 96.
%t A294888 a[n_] := DivisorSum[n, Boole[# < n && DivisorSigma[1, #] <= 2#] * #&];
%t A294888 Array[a, 100] (* _Jean-François Alcover_, Nov 17 2017 *)
%o A294888 (PARI) A294888(n) = sumdiv(n, d, (d<n)*(sigma(d)<=(2*d))*d);
%Y A294888 Cf. A001065, A263837, A294928, A294935, A294886, A294887, A294889.
%Y A294888 Cf. A294900 (fixed points).
%K A294888 nonn
%O A294888 1,4
%A A294888 _Antti Karttunen_, Nov 14 2017