cp's OEIS Frontend

A082089 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.

%I A082089 #11 May 12 2025 23:32:09
%S A082089 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 A082089 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 A082089 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 A082089 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 A082089 a(n) < n holds usually, except few large values arising unexpectedly.
%F A082089 a(n) = A000720(A082087(A000142(A000040(n)))) = pi(A082087(p(n)!)).
%e A082089 n=100, p(100)=541, starts at factorial of 100th prime and ends in 24133, the 2687th prime, so a(100)=2687;
%e A082089 n=99, initial value=523!, fixed point is 19, the 8th prime, a(99)=8.
%t A082089 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 A082089 Cf. A008472, A034387, A007504, A075860, A082087, A082088.
%K A082089 nonn
%O A082089 2,2
%A A082089 _Labos Elemer_, Apr 09 2003