A061257 Euler transform of reduced totient function psi(n), cf. A002322.

1, 1, 2, 4, 7, 13, 21, 37, 58, 96, 153, 243, 376, 584, 897, 1353, 2046, 3060, 4552, 6714, 9862, 14386, 20898, 30198, 43427, 62159, 88600, 125804, 177881, 250615, 351819, 492203, 686294, 953954, 1321902, 1826394, 2516364, 3457332, 4737576, 6475332

Offset: 0

Author

Vladeta Jovovic, Apr 21 2001

Keywords

• easy
• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A002322, A061258, A006171, A001970, A061255, A061256.

Programs

Mathematica

nn = 20; b = Table[CarmichaelLambda[n], {n, nn}]; CoefficientList[Series[Product[1/(1 - x^m)^b[[m]], {m, nn}], {x, 0, nn}], x] (* T. D. Noe, Jun 19 2012 *)

Formula

G.f.: Product_{k=1..infinity} (1 - x^k)^(-psi(k)). a(n)=1/n*Sum_{k=1..n} a(n-k)*b(k), n>1, a(0)=1, b(k)=Sum_{d|k} d*psi(d), cf. A061258.