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%I #8 Aug 23 2024 22:51:57
%S 1,3,4,7,2,13,11,3,4,3,4,45,1,60,14,4,3,3,21,1,4,4,6,3,4,3,2,4,6,2,4,
%T 4,4,4,105,4,4,3,4,4,3,4,3,4,1,4,8,2,2,19,3,1,20,14,4,20,52,4,4,977,1,
%U 3,65,1108,1,2,46,3,3,1,3,1,2,4,829,2,25,3,8,25,4,378,3,3,29,3,6,8,1,1,28
%N a(n)-th prime is the fixed point if function A008472[=sum of prime factors with no repetition] is iterated when started at factorial of n-th prime.
%C a(n)<n holds usually, except few large values arising unexpectedly.
%F a(n) = A000720(A082087(A000142(A000040(n)))) = pi(A082087(p(n)!)).
%e n=100,p(100)=541,starts at factorial of 100th prime and ends
%e in 24133, the 2687th prime, so a(100)=2687;
%e n=99, initial value=523!, fixed point is 19, the 8th prime,
%e a(99)=8.
%t 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[PrimePi[FixedPoint[sopf, Prime[w]! ]], {w, 2, 100}]
%Y Cf. A008472, A034387, A007504, A075860, A082087, A082088.
%K nonn
%O 2,2
%A _Labos Elemer_, Apr 09 2003