A307487 G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} mu(k)*x^k*A(x)^k/(1 - x^k*A(x)^k)^2, where mu() is the Möbius function (A008683).

1, 1, 2, 6, 19, 65, 231, 847, 3187, 12223, 47610, 187836, 749055, 3014453, 12226718, 49931342, 205133243, 847224291, 3515681010, 14650664552, 61286007817, 257256430363, 1083272333869, 4574656128903, 19369837160689, 82214738381631, 349743277470990

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} phi(k)*x^k*A(x)^k, where phi() is the Euler totient function (A000010).

G.f.: A(x) = (1/x)*Series_Reversion(x/(1 + Sum_{k>=1} phi(k)*x^k)).

Example

G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 19*x^4 + 65*x^5 + 231*x^6 + 847*x^7 + 3187*x^8 + 12223*x^9 + 47610*x^10 + ...

Mathematica

terms = 27; CoefficientList[1/x InverseSeries[Series[x/(1 + Sum[EulerPhi[k] x^k, {k, 1, terms}]), {x, 0, terms}], x], x]
terms = 27; A[_] = 0; Do[A[x_] = 1 + Sum[MoebiusMu[k] x^k A[x]^k/(1 - x^k A[x]^k)^2, {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
terms = 27; A[_] = 0; Do[A[x_] = 1 + Sum[EulerPhi[k] x^k A[x]^k, {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]

Crossrefs

Cf. A000010, A008683, A050391, A307488.

Sequence in context: A348848 A047016 A307354 * A212380 A150084 A275755

Adjacent sequences: A307484 A307485 A307486 * A307488 A307489 A307490

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 10 2019

Status

approved