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%I #35 Mar 30 2012 17:27:25
%S 1,3,5,7,9,12,13,16,18,20,21,25,27,28,30,32,37,43,44,45,48,49,50,52,
%T 57,60,61,64,66,67,68,70,73,75,77,78,80,81,85,87,90,91,92,97,100,101,
%U 102,104,108,110,112,115,117,126
%N Numbers not the sum of a smaller number and its prime factors (with multiplicity).
%C If a number is not squarefree, then its repeated prime factors are added as many times as the exponent indicates (e.g., the sum of prime factors of 8 is 6 since 8 = 2 * 2 * 2 and 2 + 2 + 2 = 6).
%C No even semiprime (A100484) can be in this sequence, since, if nothing else, it is the sum of a prime number and that prime number's only prime factor (itself).
%e 3 is in the sequence since neither 1 + sopfr(1) nor 2 + sopfr(2) add up to 3 (instead these equal 2 and 4 respectively).
%e Because 2 + sopfr(2) = 4, the number 4 is not in this sequence.
%t pfAddSeq[start_, max_] := NestWhileList[# + Plus@@Times@@@FactorInteger@# &, start, # < max &]; Complement[Range[200], Flatten[Table[Drop[pfAddSeq[n, 200], 1], {n, 200}]]]
%Y Cf. A096461, A192896 (only a(1) of those sequences can be in this sequence). Cf. also A001414. Analogous to A005114.
%K nonn
%O 1,2
%A _Alonso del Arte_, Jul 13 2011
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