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Sum of nonabundant proper divisors of n.
8

%I #11 Nov 17 2017 20:31:00

%S 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 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 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 Sum of nonabundant proper divisors of n.

%C Sum of divisors of n smaller than n that are nonabundant numbers (in A263837).

%H Antti Karttunen, <a href="/A294888/b294888.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>

%F a(n) = Sum_{d|n, d<n} A294935(d)*d.

%F a(n) + A294889(n) = A001065(n).

%e 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 a[n_] := DivisorSum[n, Boole[# < n && DivisorSigma[1, #] <= 2#] * #&];

%t Array[a, 100] (* _Jean-François Alcover_, Nov 17 2017 *)

%o (PARI) A294888(n) = sumdiv(n, d, (d<n)*(sigma(d)<=(2*d))*d);

%Y Cf. A001065, A263837, A294928, A294935, A294886, A294887, A294889.

%Y Cf. A294900 (fixed points).

%K nonn

%O 1,4

%A _Antti Karttunen_, Nov 14 2017