A162665 a(n) = sigma_2(n) + 3 sigma(n) tau(n) + tau(n)^3.

5, 31, 42, 111, 70, 258, 106, 329, 235, 410, 202, 930, 262, 602, 612, 931, 406, 1373, 490, 1518, 948, 1106, 682, 2802, 957, 1418, 1364, 2274, 1030, 3540, 1162, 2715, 1860, 2162, 1940, 5097, 1606, 2594, 2436, 4882, 1942, 5316, 2122, 4290, 3986, 3578, 2506

Offset: 1

Author

Franklin T. Adams-Watters, Jul 09 2009

Keywords

• nonn
• easy

Comments

Row 3 of A162663.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000203, A001157, A162663.

Programs

Mathematica

Table[DivisorSigma[2,n]+3DivisorSigma[1,n]DivisorSigma[0,n]+ DivisorSigma[ 0,n]^3,{n,50}] (* Harvey P. Dale, Jun 22 2013 *)

PARI

a(n) = my(f = factor(n), d = numdiv(f)); sigma(f, 2) + 3 * d * sigma(f) + d^3; \\ Amiram Eldar, Jan 02 2025