

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 kth positive divisor of n.


4



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
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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 A308450
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



