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A113866 Primes in the sequence A064491.

%I A113866 #15 Jul 30 2024 17:57:00
%S A113866 2,7,71,73,811,821,823,883,937,947,953,977,983,997,1031,1033,1051,
%T A113866 1063,1093,1103,1153,1171,1181,1193,1231,1277,1279,1289,1291,1297,
%U A113866 1303,1321,1381,1427,1429,1439,1451,1453,1471,1481,1483,29599,29641,29683,29717
%N A113866 Primes in the sequence A064491.
%C A113866 if the sequence of iterates hits an odd square, then the succeeding f(n) is even. The iterates will remain even until f(n) is an even square, so the sequence grows slowly for a long time, then has big 'jumps'. Is the sequence infinite?
%H A113866 Robert Israel, <a href="/A113866/b113866.txt">Table of n, a(n) for n = 1..4453</a>
%e A113866 If f(n) = n + tau(n), then the functional iterates of 7 are 7,9,12,18,24,32,38,42,50,56,64 and 71 which is prime so a(2)=7, a(3)=71
%p A113866 a:= 1: R:= NULL: count:= 0:
%p A113866 while count < 100 do
%p A113866   a:= a+numtheory:-tau(a);
%p A113866   if isprime(a) then count:= count+1; R:= R, a;  fi
%p A113866 od:
%p A113866 R; # _Robert Israel_, Nov 14 2020
%t A113866 Select[NestList[#+DivisorSigma[0, #]&, 1,2535] ,PrimeQ] (* _James C. McMahon_, Jul 07 2024 *)
%Y A113866 Cf. A064491.
%K A113866 nonn,look
%O A113866 1,1
%A A113866 _John L. Drost_, Jan 25 2006