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%I #5 Oct 15 2013 22:31:54
%S 0,2,5,11,16,7,37,149,7,27,11,11,23,2389,49,11,31,19,67,109,13,8,25,8,
%T 461,179,1319,9,193,16,7,4931,121,7,9,8,7,8,2895630887,25,19,13,19,41,
%U 2209493509721,32,5939,23,43,11
%N a(n)=A082081[n! ]=A082081[A000142[n]] Fixed points of iterated A008475 function initiated at factorials as initial values.
%e Fixed point is always a prime or a true power of prime:
%e a term from A000961.
%e n=20!=2432902008176640000, a(20)=109 because
%e fixed point list={2432902008176640000,269439,214,109}}
%t ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] ep[x_] := Table[Part[ffi[x], 2*w], {w, 1, lf[x]}] sex[x_] := Apply[Plus, ba[x]^ep[x]] Table[FixedPoint[sex, w! ], {w, 1, 128}]
%Y Cf. A001414, A056239, A008475, A082081-A082084, A000961, A000142.
%K nonn
%O 1,2
%A _Labos Elemer_, Apr 08 2003