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A082880 Largest value of A075860(j) when j runs through composite numbers between n-th and (n+1)-th primes. That is, the largest fixed-point[=prime] reached by iteration of A008472(=sum of prime factors) initiated with composite values between two consecutive primes.

%I A082880 #13 Jun 23 2025 02:59:17
%S A082880 0,2,5,7,5,3,5,13,5,7,19,7,5,13,7,31,7,7,19,5,7,43,13,19,7,13,2,5,7,
%T A082880 61,7,19,3,73,7,7,7,43,13,19,7,13,5,7,2,103,109,3,5,31,61,7,13,19,13,
%U A082880 31,7,139,19,2,73,151,7,5,3,43,13,31,19,13,181,19,13,7,193,23,199,29,103,73
%N A082880 Largest value of A075860(j) when j runs through composite numbers between n-th and (n+1)-th primes. That is, the largest fixed-point[=prime] reached by iteration of A008472(=sum of prime factors) initiated with composite values between two consecutive primes.
%F A082880 a(n) = Max_{x=1+prime(n)..prime(n+1)-1} A075860(x).
%t A082880 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[Max[0, Table[FixedPoint[sopf, w], {w, 1+Prime[n], Prime[n+1]-1}]], {n, 80}]
%Y A082880 Cf. A075860, A008472, A082087, A082088, A082881, A029908.
%K A082880 nonn
%O A082880 1,2
%A A082880 _Labos Elemer_, Apr 16 2003