A117892 Add up the positive integers which are coprime to n in order (starting at 1). a(n) is the largest such partial sum that is <= n.

1, 1, 3, 4, 3, 6, 6, 4, 7, 4, 10, 6, 10, 9, 14, 16, 15, 13, 15, 20, 20, 16, 21, 24, 23, 25, 27, 18, 28, 19, 28, 25, 27, 25, 33, 24, 36, 36, 37, 31, 36, 30, 36, 38, 33, 36, 45, 37, 48, 44, 48, 51, 45, 54, 52, 42, 48, 49, 55, 49, 55, 49, 54, 64, 63, 62, 66, 64, 61, 54, 66, 54, 66

Offset

1,3

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

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

Mathematica

f[n_] := Block[{k = 1, t, s}, While[t = Plus @@ Select[Range[k], GCD[ #, n] == 1 &]; t <= n, s = t; k++ ]; s]; Table[f[n], {n, 80}] (* Ray Chandler, Dec 11 2006 *)
lps[n_]:=Select[Reverse[Accumulate[Select[Range[n], CoprimeQ[#, n]&]]], #<=n&, 1]; Flatten[Array[lps, 80]] (* Harvey P. Dale, Nov 22 2013 *)

Crossrefs

Cf. A092933, A117893.

Sequence in context: A197699 A005092 A136195 * A286098 A074372 A331372

Adjacent sequences: A117889 A117890 A117891 * A117893 A117894 A117895

Keyword

nonn

Author

Leroy Quet, Mar 30 2006

Extensions

Extended by Ray Chandler, Dec 11 2006

Status

approved