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A082088 a(n) is the fixed point if function A008472[=sum of prime factors with no repetition] is iterated when started at initial value prime[n]!.

%I A082088 #5 Oct 15 2013 22:31:54
%S A082088 2,5,7,17,3,41,31,5,7,5,7,197,2,281,43,7,5,5,73,2,7,7,13,5,7,5,3,7,13,
%T A082088 3,7,7,7,7,571,7,7,5,7,7,5,7,5,7,2,7,19,3,3,67,5,2,71,43,7,71,239,7,7,
%U A082088 7699,2,5,313,8893,2,3,199,5,5,2,5,2,3,7,6361,3,97,5,19,97,7,2593,5,5
%N A082088 a(n) is the fixed point if function A008472[=sum of prime factors with no repetition] is iterated when started at initial value prime[n]!.
%F A082088 a(n)=A082087[A000142(p[n])].
%e A082088 n=100,p(100)=541,start at 541! and get iteration list=
%e A082088 {541!,24133} ended immediately in a(100)=24133;
%e A082088 n=99,p(99)-523,start at 523! and get a list of
%e A082088 {523!,23592,988,34,19}, a(99)=19.
%t A082088 ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] sopf[x_] := Apply[Plus, ba[x]] Table[FixedPoint[sopf, Prime[w]! ], {w, 2, 100}]
%Y A082088 Cf. A008472, A034387, A007504, A075860, A082087.
%K A082088 nonn
%O A082088 1,1
%A A082088 _Labos Elemer_, Apr 09 2003