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a(n) = smallest divisor d of n such that n <= {sum of d and all smaller divisors of n}.
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%I #23 Mar 24 2018 18:49:56

%S 1,2,3,4,5,3,7,8,9,10,11,6,13,14,15,16,17,9,19,10,21,22,23,8,25,26,27,

%T 14,29,15,31,32,33,34,35,12,37,38,39,20,41,21,43,44,45,46,47,16,49,50,

%U 51,52,53,27,55,28,57,58,59,20,61,62,63,64,65,33,67,68,69,35,71,24,73

%N a(n) = smallest divisor d of n such that n <= {sum of d and all smaller divisors of n}.

%C Original name of this sequence: a(n) is the smallest positive integer such that (sum{k|n, 1<=k<=a(n)} k) is >= n.

%H Antti Karttunen, <a href="/A125746/b125746.txt">Table of n, a(n) for n = 1..65537</a>

%e The divisors of 12 are 1,2,3,4,6,12. 1+2+3+4 = 10, which is smaller than 12; but 1+2+3+4+6 = 16, which is >= 12. So a(12) = 6.

%t f[n_] := Block[{k = 1, d = Divisors[n]},While[Sum[d[[i]], {i, k}] < n, k++ ];d[[k]]];Table[f[n], {n, 76}] (* _Ray Chandler_, Dec 06 2006 *)

%o (PARI) A125746(n) = { my(k=0,s=0); fordiv(n,d, k++; s += d; if(s>=n,return(d))); }; \\ _Antti Karttunen_, Mar 21 2018

%Y Cf. A125747, A117553, A300826 (= n/a(n)).

%K nonn

%O 1,2

%A _Leroy Quet_, Dec 05 2006

%E Extended by _Ray Chandler_, Dec 06 2006

%E Name changed by _Antti Karttunen_, Mar 21 2018