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Search: id:A075846
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| A075846 |
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Numbers n such that sopf(n) = 1/2 (sopf(n+1) + sopf(n-1)), where sopf(x) = sum of the distinct prime factors of x. |
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+0
8
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| 10, 21, 35, 82, 221, 296, 961, 2665, 12629, 13117, 30317, 54485, 99145, 125750, 132728, 142198, 156379, 185461, 225898, 241057, 265227, 265643, 280918, 281396, 284531, 326698, 379331, 393335, 400685, 437241, 437999, 548101, 584502, 641561
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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The sum of the distinct prime factors of 21 is 3 + 7 = 10; the sum of the distinct prime factors of 22 is 2 + 11 = 13; the sum of the distinct prime factors of 20 is 2 + 5 = 7; and 10 = 1/2 (13 + 7). Hence 21 belongs to the sequence.
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MATHEMATICA
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p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[3, 10^5], p[ # ] == 0.5 (p[ # + 1] + p[ # - 1]) &]
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CROSSREFS
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Cf. A008472, A075565, A075784, A076525, A076527, A076531, A076532, A076533.
Sequence in context: A072806 A051942 A082581 this_sequence A164714 A060852 A089584
Adjacent sequences: A075843 A075844 A075845 this_sequence A075847 A075848 A075849
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KEYWORD
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nonn
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Oct 18 2002
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EXTENSIONS
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Edited and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 13 2005
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