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a(1) = 1, a(n+1) = a(n) + gpf(Sum_{i=1..n} a(i)), where gpf=A006530 (greatest prime factor).
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%I #10 Dec 17 2021 08:13:35

%S 1,2,5,7,12,15,22,24,35,76,275,354,377,618,2441,2482,5855,18456,20845,

%T 46796,47605,53966,54705,182192,182355,211856,213153,214712,216985,

%U 1693212,1694413,1713714,1716967,1717074,11728681,11729202,11738033,11752860,12041999,12180558

%N a(1) = 1, a(n+1) = a(n) + gpf(Sum_{i=1..n} a(i)), where gpf=A006530 (greatest prime factor).

%H Andrew Howroyd, <a href="/A080182/b080182.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n+1) = a(n) + gpf(A080183(n)) for n > 0.

%t gpf[n_] := FactorInteger[n][[-1, 1]];

%t a[n_] := a[n] = If[n == 1, 1, a[n-1] + gpf[Sum[a[i], {i, 1, n-1}]]];

%t Array[a, 40] (* _Jean-François Alcover_, Dec 17 2021 *)

%o (PARI) \\ here b(n) is A006530(n).

%o b(n)={if(n==1, 1, my(f=factor(n)[,1]); f[#f])}

%o seq(n)={my(a=vector(n), s=1); a[1] = 1; for(n=2, n, a[n] = a[n-1] + b(s); s += a[n]); a} \\ _Andrew Howroyd_, Apr 20 2021

%Y Cf. A006530 (gpf), A080180, A080183.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Feb 05 2003

%E Terms a(30) and beyond from _Andrew Howroyd_, Apr 20 2021