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Search: id:A046363
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| A046363 |
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Nonprime numbers whose sum of prime factors is prime (counted with multiplicity). |
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+0
18
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| 6, 10, 12, 22, 28, 34, 40, 45, 48, 52, 54, 56, 58, 63, 75, 76, 80, 82, 88, 90, 96, 99, 104, 108, 117, 118, 136, 142, 147, 148, 153, 165, 172, 175, 176, 184, 198, 202, 207, 210, 214, 224, 245, 248, 250, 252, 268, 273, 274, 279, 294, 296, 298, 300, 316, 320, 325
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If prime numbers were included the sequence would be 2,3,5,6,7,10,11, 12,13,17,19,22,23,28,29,... which is A100118. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Oct 20 2007
Also: Composites with prime sum of prime factors. [Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jan 20 2009]
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EXAMPLE
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214 = 2 * 107 -> Sum of factors is 109 -> 109 is prime.
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MAPLE
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ifac := proc (n) local L, x: L := ifactors(n)[2]: map(proc (x) options operator, arrow: seq(x[1], j = 1 .. x[2]) end proc, L) end proc: a := proc (n) if isprime(n) = false and isprime(add(t, t = ifac(n))) = true then n else end if end proc: seq(a(n), n = 1 .. 350); # with help from Edwin Clark [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 21 2009]
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MATHEMATICA
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PrimeFactorsAdded[n_] := Plus @@ Flatten[Table[ #[[1]]*#[[2]], {1}] & /@ FactorInteger[n]]; GenerateA046363[n_] := Select[Range[n], PrimeQ[PrimeFactorsAdded[ # ]] && PrimeQ[ # ] == False &]; GenerateA046363[100] would give all elements of this sequence below 100. - Ryan Witko (witko(AT)nyu.edu), Mar 08 2004
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CROSSREFS
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Cf. A046364, A046365, A100118, A000040, A002808.
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KEYWORD
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nonn,new
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AUTHOR
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Patrick De Geest (pdg(AT)worldofnumbers.com), Jun 15 1998.
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EXTENSIONS
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Edited by R. J. Mathar, Nov 02 2009
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