A127791 a(1)=1; for n>1, a(n) = Sum_{k|n} (number of earlier terms which are coprime to k).

1, 2, 4, 5, 7, 16, 11, 19, 24, 26, 19, 45, 23, 40, 47, 51, 31, 74, 34, 75, 70, 64, 43, 111, 62, 77, 89, 111, 56, 150, 58, 116, 110, 97, 115, 185, 68, 110, 136, 173, 80, 212, 83, 166, 209, 132, 91, 258, 134, 187, 173, 202, 103, 278, 182, 257, 200, 168, 116, 383, 120, 177

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

Since the positive divisors of 10 are 1,2,5,10, a(10) = (the number of earlier terms coprime to 1, which is 9) + (the number of earlier terms coprime to 2, which is 5 for a(1)=1, a(4)=5, a(5)=7, a(7)=11 and a(8)=19) + (the number of earlier terms coprime to 5, which is 8 for every earlier term except a(4)=5) + (the number of earlier terms coprime to 10, which is 4) = 9 + 5 + 8 + 4 = 26.

Maple

A127791[1]:= 1:
S[1]:= {}:
for n from 2 to 1000 do
  F:= ifactors(n)[2];
  t:= 0;
  for i from 1 to n-1 do
    Fi:= remove(t -> member(t[1], S[i]), F);
    t:= t + mul(f[2]+1, f=Fi);
  od;
  A127791[n]:= t;
  S[n]:= numtheory[factorset](t);
od:
seq(A127791[n], n=1..1000); # Robert Israel, May 06 2014

Mathematica

f[l_List] := Block[{n = Length[l] + 1, d = Divisors[n], c = 0}, Do[ c += Length[Select[l, GCD[ #, d[[i]]] == 1 &]]; , {i, Length[d]}]; Append[l, c]]; Nest[f, {1}, 64] (* Ray Chandler, Feb 08 2007 *)

Crossrefs

Cf. A127792.

Sequence in context: A101724 A123210 A019277 * A290431 A220701 A005620

Adjacent sequences: A127788 A127789 A127790 * A127792 A127793 A127794

Keyword

nonn,look

Author

Leroy Quet, Jan 29 2007

Extensions

Extended by Ray Chandler, Feb 08 2007

Status

approved