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A291301 a(n) = prime that is eventually reached when x -> sigma(x)-1 is repeatedly applied to the product of the first n primes, or -1 if no prime is ever reached.

%I A291301 #20 Sep 01 2017 10:53:26
%S A291301 2,11,71,743,6911,117239,2013983,34836479,921086711,33596203871,
%T A291301 18754852859999,1306753691335679,2795529813471359,200489563747397471,
%U A291301 7143750592470475271,146095655504943513599,161739770170976834876927,543475838478389870591999,317180662337566737324195839
%N A291301 a(n) = prime that is eventually reached when x -> sigma(x)-1 is repeatedly applied to the product of the first n primes, or -1 if no prime is ever reached.
%C A291301 A subsequence of A039654.
%H A291301 Chai Wah Wu, <a href="/A291301/b291301.txt">Table of n, a(n) for n = 1..35</a>
%e A291301 2*3*5*7*11*13 = 30030 -> 96767 -> 111359 -> 117239 takes three steps to reach a prime, so a(6) = 117239.
%t A291301 p[n_]:=Times@@Prime/@Range[n]; f[n_]:=DivisorSigma[1,n]-1;
%t A291301 a[n_]:=Last[NestWhileList[f,p[n],CompositeQ]]; a/@Range[20] (* _Ivan N. Ianakiev_, Sep 01 2017 *)
%o A291301 (Python)
%o A291301 from sympy import primorial, isprime, divisor_sigma
%o A291301 def A291301(n):
%o A291301     m = primorial(n)
%o A291301     while not isprime(m):
%o A291301         m = divisor_sigma(m) - 1
%o A291301     return m # _Chai Wah Wu_, Aug 31 2017
%Y A291301 Cf. A039654, A000203, A002110, A291302 (number of steps).
%K A291301 nonn
%O A291301 1,1
%A A291301 _N. J. A. Sloane_, Aug 31 2017
%E A291301 a(10)-a(19) from _Chai Wah Wu_, Aug 31 2017