A122457 a(1)=1, a(2)=1. a(n) = the sum of the two largest earlier terms which are both coprime to n.

1, 1, 2, 2, 4, 2, 6, 2, 6, 2, 12, 2, 18, 2, 6, 2, 30, 2, 48, 2, 6, 2, 78, 2, 126, 2, 6, 2, 204, 2, 330, 2, 6, 2, 282, 2, 612, 2, 6, 2, 942, 2, 1554, 2, 6, 2, 2496, 2, 3438, 2, 6, 2, 5934, 2, 9372, 2, 6, 2, 15306, 2, 24678, 2, 6, 2, 39984, 2, 64662, 2, 6, 2, 104646, 2, 169308, 2, 6

Offset

1,3

Comments

From Robert Israel, Jun 07 2018: (Start)

For n >= 4, a(n) = 2 if n is even.

For n >= 7, a(n) == 0 (mod 6) if n is odd.

For n >= 9, a(n) = 6 if n == 3 (mod 6). (End)

Links

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

Example

a(1)=1, a(2)=1, a(3)=2, a(4)=2, a(5)=4, a(6)=2, a(8)=2 are the terms which are coprime to 9 and which occur among {a(1),a(2)...a(8)}. 2 and 4 are the two largest of these terms, so a(9) = 2 + 4 = 6.

Maple

N:= 100: # for a(1)..a(N)
V[1]:= 1: V[2]:= 1:
for n from 3 to N do
  Q:= select(t -> igcd(t, n)=1, [seq(V[i], i=1..n-1)]);
  j1:= max[index](Q);
  V[n]:= Q[j1] + max(subsop(j1=NULL, Q))
od:
seq(V[i], i=1..N); # Robert Israel, Jun 07 2018

Mathematica

f[s_] := Append[s, Plus @@ Take[Sort[Select[s, GCD[ #, Length[s] + 1] == 1 &]], -2]]; Nest[f, {1, 1}, 74] (* Ray Chandler, Sep 11 2006 *)

Crossrefs

Cf. A122456.

Sequence in context: A354875 A073348 A287093 * A319410 A337174 A139770

Adjacent sequences: A122454 A122455 A122456 * A122458 A122459 A122460

Keyword

nonn,look

Author

Leroy Quet, Sep 07 2006

Extensions

Corrected and extended by Ray Chandler and Robert G. Wilson v, Sep 11 2006

Status

approved