A092342 a(n) = sigma_3(3n+1).
1, 73, 344, 1134, 2198, 4681, 6860, 11988, 15751, 25112, 29792, 44226, 50654, 73710, 79508, 109512, 117993, 160454, 167832, 219510, 226982, 299593, 300764, 390096, 389018, 500780, 493040, 620298, 619164, 779220, 756112, 934416, 912674, 1149823, 1092728
Offset: 0
Examples
q + 73*q^4 + 344*q^7 + 1134*q^10 + 2198*q^13 + 4681*q^16 + ...
Programs
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Mathematica
DivisorSigma[3,3*Range[0,40]+1] (* Harvey P. Dale, Apr 22 2019 *)
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PARI
{a(n) = if(n<0, 0, sigma(3*n+1, 3))} /* Michael Somos, Aug 22 2007 */
Formula
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
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
Sum_{k=0..n} a(k) ~ (20*zeta(4)/3) * n^4. - Amiram Eldar, Dec 12 2023