A117893 Add up the positive integers that are coprime to n in order (starting at 1). a(n) is the smallest such partial sum that is >= n.

1, 4, 3, 4, 6, 6, 10, 9, 12, 11, 15, 13, 15, 18, 22, 16, 21, 24, 21, 20, 30, 25, 28, 24, 31, 36, 27, 29, 36, 32, 36, 36, 37, 36, 44, 37, 45, 49, 48, 44, 45, 47, 45, 53, 46, 49, 55, 54, 59, 61, 61, 68, 55, 54, 65, 57, 61, 64, 66, 68, 66, 64, 70, 64, 77, 85, 78, 83, 75, 73, 78, 73

Offset

1,2

Comments

a(2) = 1+3. Every other a(n) of the sequence involves only adding integers that are <= n.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

12 is coprime to 1, 5, 7, 11,... Now 1 = 1, 1+5 = 6, 1+5+7 = 13, 1+5+7+11 = 24, ... 13 is the smallest such partial sum that is >= 12. So a(12) = 13.

Maple

printf("1, 4, ") ; for n from 3 to 60 do resul :=0 ; for m from 1 to 1000 do if gcd(n, m) <= 1 then resul := resul + m ; if resul >= n then printf("%a, ", resul) ; break ; fi ; fi ; od : od: # R. J. Mathar, Apr 02 2006

Mathematica

f[n_] := Block[{k = 1, s}, While[s = Plus @@ Select[Range[k], GCD[ #, n] == 1 &]; s < n, k++ ]; s]; Table[f[n], {n, 75}] (* Ray Chandler, Dec 11 2006 *)

Crossrefs

Cf. A117892, A125748, A125749.

Cf. A092933.

Sequence in context: A282822 A193694 A354471 * A354346 A021701 A097511

Adjacent sequences: A117890 A117891 A117892 * A117894 A117895 A117896

Keyword

nonn

Author

Leroy Quet, Mar 30 2006

Extensions

More terms from R. J. Mathar, Apr 02 2006

a(61) and later terms from Ray Chandler, Dec 11 2006

Status

approved