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A002217
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Starting with n, repeatedly calculate the sum of prime factors (with repetition) of the previous term, until reaching 0 or a fixed point: a(n) is the number of terms in the resulting sequence.
(Formerly M0150 N0060)
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9
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2, 1, 1, 1, 1, 2, 1, 3, 3, 2, 1, 2, 1, 4, 4, 4, 1, 4, 1, 4, 3, 2, 1, 4, 3, 5, 4, 2, 1, 3, 1, 3, 5, 2, 3, 3, 1, 4, 5, 2, 1, 3, 1, 5, 2, 4, 1, 2, 5, 3, 5, 2, 1, 2, 5, 2, 3, 2, 1, 3, 1, 6, 2, 3, 5, 5, 1, 4, 6, 5, 1, 3, 1, 6, 2, 2, 5, 5, 1, 2, 3, 2, 1, 5, 3, 3, 4, 2, 1, 2, 5, 5, 3, 6, 5, 2, 1, 5, 2, 5, 1, 3, 1, 2, 5
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OFFSET
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1,1
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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EXAMPLE
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20 -> 2+2+5 = 9 -> 3+3 = 6 -> 2+3 = 5, so a(20) = length of sequence {20,9,6,5} = 4.
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MATHEMATICA
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sopfr[n_] := Times @@@ FactorInteger[n] // Total;
a[1] = 2; a[n_] := Length[ FixedPointList[sopfr, n]] - 1;
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CROSSREFS
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Cf. A001414 (sum of prime factors of n), A029908 (fixed point that is reached).
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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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