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Search: id:A029908
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| A029908 |
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Starting with n, repeatedly sum prime factors (with multiplicity) until reaching 0 or a fixed point. |
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+0
13
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| 0, 2, 3, 4, 5, 5, 7, 5, 5, 7, 11, 7, 13, 5, 5, 5, 17, 5, 19, 5, 7, 13, 23, 5, 7, 5, 5, 11, 29, 7, 31, 7, 5, 19, 7, 7, 37, 7, 5, 11, 41, 7, 43, 5, 11, 7, 47, 11, 5, 7, 5, 17, 53, 11, 5, 13, 13, 31, 59, 7, 61, 5, 13, 7, 5, 5, 67, 7, 5, 5, 71, 7, 73, 5, 13, 23, 5, 5, 79, 13, 7, 43, 83, 5, 13
(list; graph; listen)
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OFFSET
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1,2
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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.
A002217(n) is number of terms in sequence from n to a(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 08 2003
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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)=5.
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MATHEMATICA
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ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] ep[x_] := Table[Part[ffi[x], 2*w], {w, 1, lf[x]}] slog[x_] := slog[x_] := Apply[Plus, ba[x]*ep[x]] Table[FixedPoint[slog, w], {w, 1, 128}]
f[n_] := Plus @@ Flatten[ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@n]; Array[ FixedPoint[f, # ] &, 87] (from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 18 2006)
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CROSSREFS
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A001414(n) is sum of prime factors of n. Cf. A081758, A002217, A075860.
Cf. A001414, A056239, A008475, A082081, A082083.
Sequence in context: A017855 A051598 A086993 this_sequence A081758 A106492 A118503
Adjacent sequences: A029905 A029906 A029907 this_sequence A029909 A029910 A029911
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KEYWORD
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nonn
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AUTHOR
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Dann Toliver (fsdrt(AT)hotmail.com)
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