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A102128
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a(1) = 1; a(n) = sum of previous terms which divide n.
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1
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1, 1, 2, 4, 2, 6, 2, 12, 2, 10, 2, 34, 2, 14, 2, 20, 2, 24, 2, 54, 2, 22, 2, 70, 2, 26, 2, 46, 2, 46, 2, 36, 2, 68, 2, 94, 2, 38, 2, 74, 2, 62, 2, 70, 2, 138, 2, 94, 2, 60, 2, 82, 2, 114, 2, 74, 2, 58, 2, 172, 2, 124, 2, 68, 2, 94, 2, 242, 2, 234, 2, 154, 2, 222, 2, 118, 2, 110, 2, 114, 2
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OFFSET
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1,3
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LINKS
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FORMULA
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a(1) = 1; a(n) = [x^n] Sum_{k=1..n-1} a(k)*x^a(k)/(1 - x^a(k)). - Ilya Gutkovskiy, Dec 11 2017
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EXAMPLE
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Among the first 7 terms, the terms which divide 8 are 1, 1, 2, 4, 2 and 2.
So a(8) = 1 + 1 + 2 + 4 + 2 + 2 = 12.
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MATHEMATICA
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Nest[Function[{a, n}, Append[a, Total@ Select[a, Mod[n, #] == 0 &]]] @@ {#, Length@ # + 1} &, {1}, 80] (* Michael De Vlieger, Nov 13 2018 *)
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PROG
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(PARI)
up_to = 20000;
A102128list(up_to) = { my(v=vector(up_to)); v[1] = 1; for(n=2, up_to, v[n] = sum(j=1, n-1, v[j]*!(n%v[j]))); (v); };
v102128 = A102128list(up_to);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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