Search: id:A046363
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%I A046363
%S A046363 6,10,12,22,28,34,40,45,48,52,54,56,58,63,75,76,80,82,88,90,96,99,104,
%T A046363 108,117,118,136,142,147,148,153,165,172,175,176,184,198,202,207,210,
%U A046363 214,224,245,248,250,252,268,273,274,279,294,296,298,300,316,320,325
%N A046363 Nonprime numbers whose sum of prime factors is prime (counted with multiplicity).
%C A046363 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
%C A046363 Also: Composites with prime sum of prime factors. [Juri-Stepan Gerasimov 
               (2stepan(AT)rambler.ru), Jan 20 2009]
%e A046363 214 = 2 * 107 -> Sum of factors is 109 -> 109 is prime.
%p A046363 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]
%t A046363 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
%Y A046363 Cf. A046364, A046365, A100118, A000040, A002808.
%Y A046363 Sequence in context: A076763 A064712 A098669 this_sequence A101086 A074924 
               A064166
%Y A046363 Adjacent sequences: A046360 A046361 A046362 this_sequence A046364 A046365 
               A046366
%K A046363 nonn
%O A046363 1,1
%A A046363 Patrick De Geest (pdg(AT)worldofnumbers.com), Jun 15 1998.
%E A046363 Edited by R. J. Mathar, Nov 02 2009

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