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Search: id:A002217
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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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+0
5
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For n>1, the sequence reaches a fixed point, which is either 4 or a prime.
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REFERENCES
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M. Lal, Iterates of a number-theoretic function, Math. Comp., 23 (1969), 181-183.
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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T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein's World of Mathematics, Sum of Prime Factors
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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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CROSSREFS
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A001414(n) is the sum of prime factors of n. A029908(n) is the fixed point that is reached.
Sequence in context: A163768 A029434 A156281 this_sequence A157047 A059342 A062831
Adjacent sequences: A002214 A002215 A002216 this_sequence A002218 A002219 A002220
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms and better description from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 08 2003
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