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%I #21 Mar 24 2018 18:50:10
%S 1,2,2,3,2,3,2,4,3,4,2,5,2,4,4,5,2,5,2,5,4,4,2,6,3,4,4,5,2,7,2,6,4,4,
%T 4,7,2,4,4,7,2,7,2,6,6,4,2,8,3,6,4,6,2,7,4,7,4,4,2,10,2,4,6,7,4,7,2,6,
%U 4,7,2,10,2,4,6,6,4,7,2,9,5,4,2,10,4,4,4,7,2,10,4,6,4,4,4,10,2,6,6,8,2,7,2
%N a(n) is the smallest positive integer such that (Sum_{t(k)|n, 1 <= k <= a(n)} t(k)) >= n, where t(k) is the k-th positive divisor of n.
%C a(n) = the least number of divisors of n, taken in increasing order as 1, A020639(n), A292269(n), etc. needed so that their sum is >= n. - _Antti Karttunen_, Mar 21 2018
%H Antti Karttunen, <a href="/A125747/b125747.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. 6 is the 5th divisor of 12, so a(12) = 5.
%t f[n_] := Block[{k = 1, d = Divisors[n]},While[Sum[d[[i]], {i, k}] < n, k++ ];k];Table[f[n], {n, 105}] (* _Ray Chandler_, Dec 06 2006 *)
%o (PARI) A125747(n) = { my(k=0,s=0); fordiv(n,d, k++; s += d; if(s>=n,return(k))); }; \\ _Antti Karttunen_, Mar 21 2018
%Y Cf. A020639, A292269, A125746, A117553.
%K nonn
%O 1,2
%A _Leroy Quet_, Dec 05 2006
%E Extended by _Ray Chandler_, Dec 06 2006
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