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 A092342 a(n) = sigma_3(3n+1). 4

%I

%S 1,73,344,1134,2198,4681,6860,11988,15751,25112,29792,44226,50654,

%T 73710,79508,109512,117993,160454,167832,219510,226982,299593,300764,

%U 390096,389018,500780,493040,620298,619164,779220,756112,934416,912674,1149823,1092728

%N a(n) = sigma_3(3n+1).

%F Expansion of q^(-1/3) * c(q) * (c(q)^3 + b(q)^3 / 3) in powers of q where b(), c() are cubic AGM functions. - _Michael Somos_, Aug 22 2007

%F If b(3*n) = 0, b(3*n+1) = a(n), b(3*n+2) = A092343(n), then b(n) is multiplicative with b(3^e) = 0^e, b(p^e) = (p^(3*e+3) - 1) / (p^3 - 1) otherwise. - _Michael Somos_, Aug 22 2007

%F a(n) = A000731(n) + 81*A033690(n-1). - _Michael Somos_, Aug 22 2007

%e q + 73*q^4 + 344*q^7 + 1134*q^10 + 2198*q^13 + 4681*q^16 + ...

%t DivisorSigma[3,3*Range[0,40]+1] (* _Harvey P. Dale_, Apr 22 2019 *)

%o (PARI) {a(n) = if(n<0, 0, sigma(3*n+1, 3))} /* _Michael Somos_, Aug 22 2007 */

%Y Trisection of A001158. Cf. A045823, A091986, A092341, A092343.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Mar 20 2004

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)