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A082588
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a(1) = 1, a(n) = Sum_{d | n and d < n} a(d)^2 for n > 1.
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5
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1, 1, 1, 2, 1, 3, 1, 6, 2, 3, 1, 16, 1, 3, 3, 42, 1, 16, 1, 16, 3, 3, 1, 308, 2, 3, 6, 16, 1, 31, 1, 1806, 3, 3, 3, 532, 1, 3, 3, 308, 1, 31, 1, 16, 16, 3, 1, 96936, 2, 16, 3, 16, 1, 308, 3, 308, 3, 3, 1, 1508, 1, 3, 16, 3263442, 3, 31, 1, 16, 3, 31, 1, 378456
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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a(12) = a(1)^2 + a(2)^2 + a(3)^2 + a(4)^2 + a(6)^2 = 1^2 + 1^2 + 1^2 + 2^2 + 3^2 = 1 + 1 + 1 + 4 + 9 = 16.
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MATHEMATICA
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a[ n_] := If[ n < 2, Boole[n == 1], Sum[ a[d]^2, {d, Drop[Divisors @ n, -1]}]]; (* Michael Somos, May 19 2018 *)
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PROG
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(Python)
a = [1]
for n in range(2, 10001):
a.append(sum(a[d-1]**2 for d in range(1, n) if n%d == 0))
print(a)
(PARI) a(n) = if (n==1, 1, sumdiv(n, d, if (d<n, a(d)^2))); \\ Michel Marcus, Jan 30 2017
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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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