A061255 Euler transform of Euler totient function phi(n), cf. A000010.

1, 1, 2, 4, 7, 13, 21, 37, 60, 98, 157, 251, 392, 612, 943, 1439, 2187, 3293, 4930, 7330, 10839, 15935, 23315, 33933, 49170, 70914, 101861, 145713, 207638, 294796, 417061, 588019, 826351, 1157651, 1616849, 2251623, 3126775, 4330271, 5981190

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe)

N. J. A. Sloane, Transforms

Formula

G.f.: Product_{k>=1} (1 - x^k)^(-phi(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*phi(d), cf. A057660.

Logarithmic derivative yields A057660 (equivalent to above formula). - Paul D. Hanna, Sep 05 2012

a(n) ~ exp(3^(4/3) * Zeta(3)^(1/3) * n^(2/3) / (2^(1/3) * Pi^(2/3)) - 1/6) * A^2 * Zeta(3)^(1/9) / (2^(4/9) * 3^(7/18) * Pi^(8/9) * n^(11/18)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Mar 23 2018

G.f.: exp(Sum_{k>=1} (sigma_2(k^2)/sigma_1(k^2)) * x^k/k). - Ilya Gutkovskiy, Apr 22 2019

Mathematica

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

Crossrefs

Cf. A000010, A057660, A006171, A001970, A061256, A061257, A299069, A318975.

Sequence in context: A018150 A019471 A061257 * A088111 A325864 A143823

Adjacent sequences: A061252 A061253 A061254 * A061256 A061257 A061258

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 21 2001

Status

approved