%I #9 Feb 05 2020 09:45:40
%S 1,6,126,198,1433322,317533782,386625738,451240398,394171702494,
%T 701463692694,2111238978018
%N Numbers k such that A331694(k) = k.
%C Is this sequence finite?
%C a(12) > 3*10^12. It appears that if p>43, p+4, and q=(4p^2+18p-1)/21 are 3 primes, then 6*p*(p+4)*q is a term, so the sequence is probably infinite. Terms of this form are a(6), a(10), 27022402862934, 815943210142422,... Other terms, not of this form, are 74704831120974, 76402543308186, 144328894843494,... - _Giovanni Resta_, Feb 04 2020
%H Rémy Sigrist, <a href="/A331837/a331837.png">Logarithmic line plot of the sequence {e_k} associated to 451240398</a>
%e For n = 126, we have (with the notations introduced in A331694):
%e k e_k d_k
%e -- --- ---
%e 0 0 N/A
%e 1 1 1
%e 2 3 2
%e 3 0 3
%e 4 6 6
%e 5 13 7
%e 6 4 9
%e 7 18 14
%e 8 0 18
%e 9 21 21
%e 10 63 42
%e 11 0 63
%e 12 126 126
%e - so 126 is a term.
%o (PARI) is(n) = my (e=0); fordiv (n, d, if (e>=d, e-=d, e+=d)); e==n
%Y Cf. A331694.
%K nonn,more
%O 1,2
%A _Rémy Sigrist_, Jan 28 2020
%E a(9)-a(11) from _Giovanni Resta_, Feb 04 2020