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A348337
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For n >= 1; x = n, then iterate x --> x + d(x) until d(x + d(x)) >= d(x). a(n) gives the number of iteration steps where d(i) is the number of divisors of i, A000005(i).
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0
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3, 2, 7, 1, 6, 5, 5, 4, 4, 4, 3, 3, 2, 3, 1, 1, 3, 2, 2, 1, 1, 3, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 1, 2, 2, 1, 2, 3, 1, 2, 3, 1, 3, 3, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 3, 3, 6, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 3, 5, 2, 2, 1, 1, 2, 1, 2, 2, 1, 3, 2, 4, 1, 2, 5, 4, 5, 1, 4, 4, 1, 4, 3, 3, 3, 3, 2, 1
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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n = 1; x(1) = 1 + d(1) = 2, d(1 + d(1)) >= d(1) thus x(2) = 2 + d(2) = 4, d(2 + d(2)) >= d(2) thus x(3) = 4 + d(4) = 7, d(4 + d(4)) < d(4), stop. a(1) = 3.
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MATHEMATICA
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d[n_] := DivisorSigma[0, n]; x[n_] := n + d[n]; a[n_] := Length@ NestWhileList[x, n, d[#] <= d[x[#]] &]; Array[a, 100] (* Amiram Eldar, Oct 15 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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