OFFSET
1,3
COMMENTS
a(n+1) = a(n) if and only if n is 1 or an odd prime (A006005). - Robert Israel, Dec 22 2016
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Feb 20 2007
EXTENSIONS
Extended by Ray Chandler, Mar 03 2007
STATUS
approved