A092341 -id:A092341 - cp's OEIS frontend

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

N. J. A. Sloane, Mar 20 2004

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

Trisection of A001158.

Cf. A000731, A013662, A033690, A045823, A091986, A092341, A092343.

DivisorSigma[3,3*Range[0,40]+1] (* Harvey P. Dale, Apr 22 2019 *)

{a(n) = if(n<0, 0, sigma(3*n+1, 3))} /* Michael Somos, Aug 22 2007 */

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
a(n) = A000731(n) + 81*A033690(n-1). - Michael Somos, Aug 22 2007
Sum_{k=0..n} a(k) ~ (20*zeta(4)/3) * n^4. - Amiram Eldar, Dec 12 2023

A092343 a(n) = sigma_3(3n+2).

Original entry on oeis.org

9, 126, 585, 1332, 3096, 4914, 9198, 12168, 19782, 24390, 37449, 43344, 61740, 68922, 97236, 103824, 141759, 148878, 201240, 205380, 268128, 276948, 358722, 357912, 455886, 458208, 589806, 571788, 715572, 704970, 888264, 864360, 1061937, 1030302, 1285830

Offset: 0

N. J. A. Sloane, Mar 20 2004

			G.f. = 9 + 126*x + 585*x^2 + 1332*x^3 + 3096*x^4 + 4914*x^5 + 9198*x^6 + 12168*x^7 + ...
G.f. = 9*q^2 + 126*q^5 + 585*q^8 + 1332*q^11 + 3096*q^14 + 4914*q^17 + 9198*q^20 + ...

Trisection of A001158.

Cf. A013662, A045823, A091986, A092341, A092342, A144614.

Table[DivisorSigma[3,3n+2],{n,0,40}] (* Harvey P. Dale, Jul 02 2011 *)

{a(n) = if( n<0, 0, sigma( 3*n + 2, 3))}; /* Michael Somos, May 30 2012 */

Expansion of q^(-2/3) * (a(q) * c(q))^2 in powers of q where a(), c() are cubic AGM theta functions. - Michael Somos, May 30 2012
Convolution square of A144614. - Michael Somos, May 30 2012
Sum_{k=0..n} a(k) ~ (20*zeta(4)/3) * n^4. - Amiram Eldar, Dec 12 2023

cp's OEIS Frontend

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

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