login
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.
5
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
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
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