A125749 a(n) is the smallest positive integer such that (Sum_{1<=k<=a(n), gcd(t(k),n)=1} t(k)) is >= n, where t(k) is the k-th positive integer which is coprime to n.

1, 2, 2, 2, 3, 2, 4, 3, 4, 3, 5, 3, 5, 4, 5, 4, 6, 4, 6, 4, 6, 5, 7, 4, 7, 6, 6, 5, 8, 4, 8, 6, 7, 6, 8, 5, 9, 7, 8, 6, 9, 5, 9, 7, 7, 7, 10, 6, 10, 7, 9, 8, 10, 6, 10, 7, 9, 8, 11, 6, 11, 8, 9, 8, 11, 7, 12, 9, 10, 7, 12, 7, 12, 9, 9, 9, 12, 7, 13, 8, 11, 10, 13, 7, 12, 10, 11, 9, 13, 7, 13, 10, 12

Offset

1,2

Links

Table of n, a(n) for n=1..93.

Example

The positive integers which are coprime to 12 are 1,5,7,11,13,... Now 1+5 = 6, which is less than 12; but 1+5+7 is 13, which is >= 12. 7 is the 3rd positive integer which is coprime to 12, so a(12) = 3.

Mathematica

f[n_] := Block[{k = 1, l}, While[l = Select[Range[k], GCD[ #, n] == 1 &]; Plus @@ l < n, k++ ]; Length[l]]; Table[f[n], {n, 100}] (* Ray Chandler, Dec 11 2006 *)

Crossrefs

Cf. A125748, A117893.

Sequence in context: A364421 A352631 A134446 * A014085 A248891 A171239

Adjacent sequences: A125746 A125747 A125748 * A125750 A125751 A125752

Keyword

nonn

Author

Leroy Quet, Dec 06 2006

Extensions

Extended by Ray Chandler, Dec 11 2006

Status

approved