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A126793 a(1) = 1; a(n+1) = Sum_{k|n} floor(a(k)/a(n/k)). 1
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

Cf. A006005.

Sequence in context: A025147 A032230 A238789 * A069910 A026797 A008484

Adjacent sequences:  A126790 A126791 A126792 * A126794 A126795 A126796

KEYWORD

nonn

AUTHOR

Leroy Quet, Feb 20 2007

EXTENSIONS

Extended by Ray Chandler, Mar 03 2007

STATUS

approved

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Last modified November 13 01:32 EST 2018. Contains 317118 sequences. (Running on oeis4.)