A125746 a(n) = smallest divisor d of n such that n <= {sum of d and all smaller divisors of n}.

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, 14, 29, 15, 31, 32, 33, 34, 35, 12, 37, 38, 39, 20, 41, 21, 43, 44, 45, 46, 47, 16, 49, 50, 51, 52, 53, 27, 55, 28, 57, 58, 59, 20, 61, 62, 63, 64, 65, 33, 67, 68, 69, 35, 71, 24, 73

Offset: 1

Author

Leroy Quet, Dec 05 2006

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

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

Programs

Mathematica

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 *)

PARI

A125746(n) = { my(k=0,s=0); fordiv(n,d, k++; s += d; if(s>=n,return(d))); }; \\ Antti Karttunen, Mar 21 2018

Extensions

Extended by Ray Chandler, Dec 06 2006

Name changed by Antti Karttunen, Mar 21 2018