A126793 a(1) = 1; a(n+1) = Sum_{k|n} floor(a(k)/a(n/k)).

1, 1, 2, 2, 3, 3, 5, 5, 7, 8, 11, 11, 16, 16, 21, 22, 28, 28, 36, 36, 45, 47, 58, 58, 72, 73, 89, 92, 110, 110, 137, 137, 161, 166, 194, 195, 232, 232, 268, 276, 317, 317, 371, 371, 423, 435, 493, 493, 568, 569, 643, 657, 738, 738, 843, 846, 948, 966, 1076, 1076, 1219, 1219

Offset: 1

Author

Leroy Quet, Feb 20 2007

Keywords

• nonn

Comments

a(n+1) = a(n) if and only if n is 1 or an odd prime (A006005). - Robert Israel, Dec 22 2016

Examples

			a(13) = sum{k|12} [a(k)/a(12/k)] = [a(1)/a(12)] + [a(2)/a(6)] + [a(3)/a(4)] + [a(4)/a(3)] + [a(6)/a(2)] + [a(12)/a(1)] = [1/11] + [1/3] + [2/2] + [2/2] + [3/1] + [11/1] = 0 +0 +1 +1 +3 +11 = 16.
		

Links

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

Crossrefs

Cf. A006005.

Programs

Maple

A[1]:= 1:
for n from 1 to 100 do
  A[n+1] := add(floor(A[k]/A[n/k]),k=numtheory:-divisors(n))
od:
seq(A[i],i=1..100); # Robert Israel, Dec 22 2016

Mathematica

f[l_List] := Block[{n = Length[l], d = Divisors[n]},Append[l, Sum[ Floor[l[[d[[k]]]]/l[[n/d[[k]]]]], {k, Length[d]}]]];Nest[f, {1}, 61] (* Ray Chandler, Mar 03 2007 *)
a[1] = 1; a[n_] := a[n] = Sum[Floor[a[k]/a[(n - 1)/k]], {k, Divisors[n - 1]}]; Array[a, 62] (* Michael De Vlieger, Dec 22 2016 *)

Extensions

Extended by Ray Chandler, Mar 03 2007