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a(0) = 1; a(n) = sum of a(j)'s, j<n, where n is divisible by a(j).
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%I #17 Jun 12 2024 23:30:28

%S 1,1,2,2,6,2,14,2,10,2,22,2,20,2,30,2,18,2,44,2,52,2,46,2,32,2,28,2,

%T 72,2,78,2,66,2,36,2,98,2,40,2,112,2,64,2,112,2,94,2,56,2,62,2,106,2,

%U 80,2,156,2,60,2,188,2,126,2,162,2,162,2,70,2,166,2,206,2,76,2,154,2,164,2

%N a(0) = 1; a(n) = sum of a(j)'s, j<n, where n is divisible by a(j).

%C a(2j+1) = 2 for j > 0; a(j) is even for j > 1.

%H John Tyler Rascoe, <a href="/A055934/b055934.txt">Table of n, a(n) for n = 0..10000</a>

%e a(10) =22 because a(0), a(1), a(2), a(3), a(5), a(7), a(8) and a(9) all divide 10 and a(0) +a(1) +a(2) +a(3) +a(5) +a(7) +a(8) +a(9) = 1 + 1 +2 +2 +2 +2 + 10 +2 =22.

%o (Python)

%o def A055934_list(nmax):

%o A = [1,1]

%o for n in range(2,nmax+1):

%o if n%2 > 0:

%o A.append(2)

%o else:

%o A.append(sum(i for i in A if n%i < 1))

%o return A # _John Tyler Rascoe_, Jun 12 2024

%Y Cf. A055935.

%K easy,nonn

%O 0,3

%A _Leroy Quet_, Jul 17 2000