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

1, 1, 3, 21, 155, 2691, 18924, 732230, 9223166, 269544904, 4308339664, 264486350330, 3252603264996, 283488024709418, 5058264756924275, 239269507574263597, 9478611818612363119, 788664781674375008343, 13928483471031628860556, 1889997256419148641470346

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Example

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

Prog

 (PARI) {A226561(n)=sumdiv(n, d, d*eulerphi(d^n))}
{a(n)=polcoeff(exp(sum(k=1, n, A226561(k)*x^k/k)+x*O(x^n)), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A226561, A226458.

Sequence in context: A229809 A074575 A091171 * A026333 A370170 A205773

Adjacent sequences: A226557 A226558 A226559 * A226561 A226562 A226563

Keyword

nonn

Author

Paul D. Hanna, Jun 10 2013

Status

approved