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A075784
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Numbers n such that sopf(n) = sopf(n-1) + sopf(n-2) + sopf(n-3), where sopf(x) = sum of the distinct prime factors of x.
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8
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23156, 59785, 72521, 98426, 362231, 480223, 506123, 1049790, 1077252, 1133953, 1202068, 1277411, 1327229, 1627040, 2200058, 2317712, 2368026, 3610497, 4174012, 5668196, 6302128, 6324778, 6946075, 7179599, 7786163, 8053816
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OFFSET
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1,1
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..2400
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EXAMPLE
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The sum of the distinct prime factors of 23156 is 2 + 7 + 827 = 836; the sum of the distinct prime factors of 23155 is 5 + 11 + 421 = 437; the sum of the distinct prime factors of 23154 is 2 + 3 + 17 + 227 = 249; the sum of the distinct prime factors of 23153 is 13 + 137 = 150; and 836 = 437 + 249 + 150. Hence 23156 belongs to the sequence.
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MATHEMATICA
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p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[5, 10^5], p[ # - 1] + p[ # - 2] + p[ # - 3] == p[ # ] &]
Flatten[Position[Partition[Table[Total[FactorInteger[n][[All, 1]]], {n, 8054000}], 4, 1], _?(Total[Most[#]]==Last[#]&)]//Quiet]+3 (* Harvey P. Dale, Feb 22 2020 *)
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CROSSREFS
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Cf. A008472, A075565, A075846, A076525, A076527, A076531, A076532, A076533.
Sequence in context: A230791 A087425 A031648 * A126301 A205176 A205275
Adjacent sequences: A075781 A075782 A075783 * A075785 A075786 A075787
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KEYWORD
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nonn
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AUTHOR
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Joseph L. Pe, Oct 18 2002
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EXTENSIONS
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Edited and extended by Ray Chandler, Feb 13 2005
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STATUS
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approved
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