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A061255 Euler transform of Euler totient function phi(n), cf. A000010. 27
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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A018150 A019471 A061257 * A088111 A325864 A143823
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Apr 21 2001
STATUS
approved

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Last modified February 21 03:04 EST 2024. Contains 370219 sequences. (Running on oeis4.)