%I #7 Aug 12 2023 00:48:29
%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 42,1,31,15,20,13,25,1,22,17,30,1,54,1,40,33,26,1,64,8,43,21,46,1,48,
%U 17,64,23,32,1,46,1,34,41,63,19,78,1,58,27,74,1,93,1
%N a(n) = Sum_{d|n, d < n, d in S} d, where S is the set defined in A118372.
%C First differs from A294888 at n = 48.
%H Amiram Eldar, <a href="/A364858/b364858.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) <= A001065(n).
%F a(n) <= n if and only if n is in the set S.
%F a(n) = n if and only if n is S-perfect (A118372).
%F a(n) > n if and only if n is S-abundant (A181487).
%t seq[nmax_] := Module[{s = {1}, a = {0}, sum}, Do[sum = Total[Select[Divisors[n], MemberQ[s, #] &]]; If[sum <= n, AppendTo[s, n]]; AppendTo[a, sum], {n, 2, nmax}]; a]; seq[100]
%o (PARI) lista(nmax) = {my(c = 0, s); print1(0, ", "); for(n=2, nmax, s = sumdiv(n, d, !bittest(c, d)*d) - n; if(s > n, c+=1<<n); print1(s,", "));} \\ after _M. F. Hasler_ at A181487
%Y Cf. A001065, A118372, A181487, A294888.
%K nonn
%O 1,4
%A _Amiram Eldar_, Aug 11 2023