A179114 G.f.: A(x) = exp( Sum_{n>=1} A179115(n)*x^n/n ), where A179115(n) = Sum_{d|n} phi(d^tau(d)).

1, 1, 2, 4, 13, 19, 103, 131, 515, 777, 2183, 3387, 92950, 98220, 215084, 407878, 1321714, 1941644, 10099460, 13008998, 49257496, 74663830, 209907775, 326405877, 5955260642, 6463849558, 14769440215, 27326857279, 88012522809

Offset

0,3

Comments

phi(n) = A000010(n) is the Euler totient function of n.

tau(n) = A000005(n) is the number of divisors of n.

Links

Table of n, a(n) for n=0..28.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 13*x^4 + 19*x^5 + 103*x^6 +...
log(A(x)) = x + 3*x^2/2 + 7*x^3/3 + 35*x^4/4 + 21*x^5/5 + 441*x^6/6 +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sumdiv(m, d, eulerphi(d^sigma(d, 0)))*x^m/m)+x*O(x^n)), n)}

Crossrefs

Cf. A179115, A000010 (phi), A000005 (tau).

Sequence in context: A240096 A018761 A276118 * A356288 A082015 A362263

Adjacent sequences: A179111 A179112 A179113 * A179115 A179116 A179117

Keyword

nonn

Author

Paul D. Hanna, Jul 10 2010

Status

approved