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%I #7 Feb 05 2017 13:22:49
%S 2,6,8,9,14,25,26,30,32,38,40,45,56,63,66,70,74,75,81,86,88,96,99,100,
%T 104,117,121,130,134,136,138,144,147,153,154,158,160,168,174,184,190,
%U 194,196,206,207,216,218,238,248,250,252,254,266,275,279,280,286,289
%N Numbers n such that, in prime decomposition of n, sum of all prime factors and their orders is prime.
%C Corresponding primes in A107738. Cf. A008474 If n = Product (p_j^k_j) then a(n) = Sum (p_j + k_j).
%H Harvey P. Dale, <a href="/A107737/b107737.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFactorization.html">Prime Factorization</a>
%e n = 104 OK because 104 = 2^3 * 13^1 => (2+3)+(13+1) = 19 is prime.
%t ta=Table[Plus @@ Flatten[FactorInteger[n]], {n, 300}];bb={};Do[If[PrimeQ[t=ta[[i]]], bb=Append[bb, {i, t}]], {i, 300}];tr=Transpose[bb];A107738=tr[[2]];A107737=tr[[1]]
%t Select[Range[2,300],PrimeQ[Total[Flatten[FactorInteger[#]]]]&] (* _Harvey P. Dale_, Feb 05 2017 *)
%Y Cf. A008474, A107738.
%K nonn
%O 1,1
%A _Zak Seidov_, May 23 2005
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