A128332 - OEIS

1, 1, 1, 2, 3, 4, 6, 3, 6, 6, 3, 8, 11, 13, 5, 5, 6, 16, 8, 7, 11, 7, 7, 10, 23, 15, 12, 18, 7, 24, 30, 11, 32, 33, 26, 35, 36, 37, 38, 21, 40, 41, 28, 28, 19, 45, 23, 23, 23, 24, 49, 51, 21, 18, 33, 35, 26, 57, 58, 46, 28, 30, 30, 17, 63, 26, 66, 33, 42, 37, 70, 71, 47, 36, 74, 28

EXAMPLE

a(5) + a(6) = 10. The number of positive integers <= 7 that are coprime to 10 is three, these integers being 1, 3 and 7. So a(7) = 3.

MAPLE

a[0]:=1: a[1]:=1: for n from 2 to 100 do ct:=0: for j from 1 to n do if igcd(j, a[n-1]+a[n-2])=1 then ct:=ct+1 else fi od: a[n]:=ct: od: seq(a[n], n=0..100); # Emeric Deutsch, May 07 2007

MATHEMATICA

nxt[{n_, a_, b_}]:={n+1, b, Count[Range[n+1], _?(CoprimeQ[a+b, #]&)]}; Transpose[ NestList[ nxt, {1, 1, 1}, 80]][[2]] (* Harvey P. Dale, Jan 21 2015 *)

CROSSREFS

Cf. A000010 (number of positive numbers <= n that are coprime to n).