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%I #4 Oct 29 2017 08:32:27
%S 1,1,8,182,6962,419242,36634192,4488812596,722684103164,
%T 148732979255324,38081859158891744,11886289198519022344,
%U 4436616366171778495192,1951865016371020657730488,999444614538375532106921408,589291073127565867170680837168,396337742242710677353781867268368,301596359950397359016053774993717264,257797318556710190428189878485023244416
%N E.g.f.: exp( Sum_{n>=1} phi(n) * sigma(n^n) * x^n/n ).
%C Note that exp( Sum_{n>=1} phi(K) * sigma(K^n) * x^n/n ) is an integer series for any fixed positive integer K ; though similar, the generating function for this sequence does not yield an integer series.
%H Paul D. Hanna, <a href="/A294355/b294355.txt">Table of n, a(n) for n = 0..200</a>
%e E.g.f.: A(x) = 1 + x + 8*x^2/2! + 182*x^3/3! + 6962*x^4/4! + 419242*x^5/5! + 36634192*x^6/6! + 4488812596*x^7/7! + 722684103164*x^8/8! + 148732979255324*x^9/9! + 38081859158891744*x^10/10! +...
%e such that
%e log(A(x)) = x + phi(2)*sigma(2^2)*x^2/2 + phi(3)*sigma(3^3)*x^3/3 + phi(4)*sigma(4^4)*x^4/4 + phi(5)*sigma(5^5)*x^5/5 + phi(6)*sigma(6^6)*x^6/6 + phi(7)*sigma(7^7)*x^7/7 +...+ phi(n)*sigma(n^n)*x^n/n +...
%e Explicitly,
%e log(A(x)) = x + 7*x^2/2 + 80*x^3/3 + 1022*x^4/4 + 15624*x^5/5 + 277622*x^6/6 + 5764800*x^7/7 + 134217724*x^8/8 + 3486784398*x^9/9 + 99951169828*x^10/10 +...
%o (PARI) {a(n) = my(A); A = exp(sum(m=1,n+1, eulerphi(m)*sigma(m^m)*x^m/m) +x*O(x^n)); n!*polcoeff(A,n)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A000010 (phi), A000203 (sigma).
%K nonn
%O 0,3
%A _Paul D. Hanna_, Oct 29 2017
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