A125747 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.

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, 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, 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

Offset

1,2

Comments

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

Links

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

Example

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.

Mathematica

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 *)

Prog

(PARI) A125747(n) = { my(k=0, s=0); fordiv(n, d, k++; s += d; if(s>=n, return(k))); }; \\ Antti Karttunen, Mar 21 2018

Crossrefs

Cf. A020639, A292269, A125746, A117553.

Sequence in context: A166469 A080226 A060741 * A060129 A327161 A350067

Adjacent sequences: A125744 A125745 A125746 * A125748 A125749 A125750

Keyword

nonn

Author

Leroy Quet, Dec 05 2006

Extensions

Extended by Ray Chandler, Dec 06 2006

Status

approved