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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 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

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