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Least solution to cototient(x) = n!, where cototient(x) = x-phi(x).
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%I #10 Aug 24 2019 11:58:34

%S 2,4,10,36,168,1008,7056,56448,470400,4704000,51528960,618347520,

%T 7740902400,108372633600

%N Least solution to cototient(x) = n!, where cototient(x) = x-phi(x).

%C a(15) <= 1625589504000. a(16) <= 26009432064000. a(17) <= 442160345088000. [_Donovan Johnson_, Feb 05 2010]

%F a(n) = Min{x; x-A000010(x)=n!} = Min{A051953(x)=A000142(n)}.

%e Solutions to x-Phi[x]=720 are {1008,1424,1432,1436,1438} of which the smallest is a(6)=1008.

%o (PARI) a(n) = my(x=1); while(x-eulerphi(x) != n!, x++); x; \\ _Michel Marcus_, Aug 24 2019

%Y Cf. A000010, A051953, A000142, A055487.

%K nonn,more

%O 1,1

%A _Labos Elemer_, Dec 10 2001

%E a(12)-a(14) from _Donovan Johnson_, Feb 05 2010