A076334 Differences between successive squarefree kernels.

1, 1, -1, 3, 1, 1, -5, 1, 7, 1, -5, 7, 1, 1, -13, 15, -11, 13, -9, 11, 1, 1, -17, -1, 21, -23, 11, 15, 1, 1, -29, 31, 1, 1, -29, 31, 1, 1, -29, 31, 1, 1, -21, -7, 31, 1, -41, 1, 3, 41, -25, 27, -47, 49, -41, 43, 1, 1, -29, 31, 1, -41, -19, 63, 1, 1, -33, 35, 1, 1, -65, 67, 1, -59, 23, 39

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A007947(n+1) - A007947(n).

G.f.: -1 + (1 - x)*Sum_{k>=1} phi(k)*mu(k)^2*x^(k-1)/(1 - x^k). - Ilya Gutkovskiy, Apr 15 2017

Mathematica

Drop[CoefficientList[Series[-1 + (1 - x)*Sum[EulerPhi[k] MoebiusMu[k]^2*x^(k - 1)/(1 - x^k), {k, 100}], {x, 0, 100}], x], 1] (* Indranil Ghosh, Apr 16 2017 *)

Prog

(PARI) x='x+O('x^100); Vec(-1 + (1 - x)*sum(k=1, 100, eulerphi(k)*moebius(k)^2*x^(k - 1)/(1 - x^k))) \\ Indranil Ghosh, Apr 16 2017

Crossrefs

Cf. A007947.

Sequence in context: A201669 A069002 A245369 * A348641 A014475 A358612

Adjacent sequences: A076331 A076332 A076333 * A076335 A076336 A076337

Keyword

sign

Author

Reinhard Zumkeller, Nov 06 2002

Status

approved