A100676 a(1) = 1; a(n+1) = Sum_{k=1..n} a(gcd(a(k),n)).

1, 1, 2, 3, 4, 5, 7, 13, 10, 10, 31, 11, 15, 27, 20, 48, 67, 17, 33, 19, 66, 33, 144, 23, 81, 40, 40, 120, 48, 29, 146, 176, 260, 878, 100, 71, 176, 37, 70, 78, 420, 41, 144, 43, 274, 172, 189, 47, 407, 73, 209, 132, 266, 53, 235, 364, 478, 169, 105, 59, 411, 61, 207, 479

Offset: 1

Author

Leroy Quet, Dec 06 2004

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A056144.

Programs

Maple

a[1]:=1: for n from 2 to 75 do b[n]:=[seq(a[gcd(a[k],n-1)],k=1..n-1)]: a[n]:=sum(b[n][j],j=1..nops(b[n])) od: seq(a[n],n=1..75);

Mathematica

a[1] = 1; a[n_] := a[n] = Plus @@ a /@ GCD[Table[a[i], {i, n - 1}], n - 1]; Table[ a[n], {n, 64}] (* Robert G. Wilson v, Dec 09 2004 *)

PARI

first(n)=my(v=vector(n)); v[1]=1; for(i=1,n-1,v[i+1]=sum(k=1,i,v[gcd(v[k],i)])); v \\ Charles R Greathouse IV, Apr 05 2016

Extensions

More terms from Emeric Deutsch and Robert G. Wilson v, Dec 09 2004