A294886 - OEIS

%I #14 Mar 14 2024 03:48:55

%S 0,1,1,3,1,6,1,7,4,8,1,10,1,10,9,15,1,15,1,22,11,14,1,18,6,16,13,28,1,

%T 36,1,31,15,20,13,19,1,22,17,30,1,48,1,40,33,26,1,34,8,43,21,46,1,42,

%U 17,36,23,32,1,40,1,34,41,63,19,72,1,58,27,74,1,27,1,40,49,64,19,84,1,46,40,44,1,52,23,46,33,92,1,90,21

%N Sum of deficient proper divisors of n.

%C Sum of divisors of n smaller than n that are deficient numbers (in A005100).

%H Antti Karttunen, <a href="/A294886/b294886.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} A294934(d)*d.

%F a(n) = A187793(n) - (A294934(n)*n).

%F a(n) + A294887(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, 9, 10, 15 and 45 are in A005100, thus a(90) = 1+2+3+5+9+10+15+45 = 90.

%t a[n_] := DivisorSum[n, # &, # < n && DivisorSigma[1, #] < 2*# &]; Array[a, 100] (* _Amiram Eldar_, Mar 14 2024 *)

%o (PARI) A294886(n) = sumdiv(n, d, (d<n)*(sigma(d)<(2*d))*d);

%Y Cf. A001065, A005100, A001065, A187793, A294926, A294934, A294887, A294888, A294889.

%Y Cf. A125310 (fixed points).

%K nonn

%O 1,4

%A _Antti Karttunen_, Nov 14 2017