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 A226560 exp( Sum_{n>=1} A226561(n)*x^n/n ), where A226561(n) = Sum_{d|n} d^n*phi(d). 2

%I #4 Jun 10 2013 20:26:17

%S 1,1,3,21,155,2691,18924,732230,9223166,269544904,4308339664,

%T 264486350330,3252603264996,283488024709418,5058264756924275,

%U 239269507574263597,9478611818612363119,788664781674375008343,13928483471031628860556,1889997256419148641470346

%N exp( Sum_{n>=1} A226561(n)*x^n/n ), where A226561(n) = Sum_{d|n} d^n*phi(d).

%e G.f.: A(x) = 1 + x + 3*x^2 + 21*x^3 + 155*x^4 + 2691*x^5 + 18924*x^6 +...

%e where

%e log(A(x)) = x + 5*x^2/2 + 55*x^3/3 + 529*x^4/4 + 12501*x^5/5 + 94835*x^6/6 + 4941259*x^7/7 + 67240193*x^8/8 +...+ A226561(n)*x^n/n +...

%o (PARI) {A226561(n)=sumdiv(n, d, d*eulerphi(d^n))}

%o {a(n)=polcoeff(exp(sum(k=1,n,A226561(k)*x^k/k)+x*O(x^n)),n)}

%o for(n=0,30,print1(a(n),", "))

%Y Cf. A226561, A226458.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jun 10 2013

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Last modified March 3 10:27 EST 2024. Contains 370510 sequences. (Running on oeis4.)