A072861 a(n) = sigma(n)^2.

1, 9, 16, 49, 36, 144, 64, 225, 169, 324, 144, 784, 196, 576, 576, 961, 324, 1521, 400, 1764, 1024, 1296, 576, 3600, 961, 1764, 1600, 3136, 900, 5184, 1024, 3969, 2304, 2916, 2304, 8281, 1444, 3600, 3136, 8100, 1764, 9216, 1936, 7056, 6084, 5184, 2304, 15376, 3249

Offset: 1

Author

N. J. A. Sloane, Jul 26 2002

Keywords

• nonn
• mult

References

• S. Ramanujan, Some formulas in the analytic theory of numbers, Mess. Math. 45 (1915), 81-84, eq. 15. (Reprinted in Collected Papers of Srinivasa Ramanujan, Chelsea Publ., New York 1962, 133-135)

Links

• J. G. Wurtzel, Table of n, a(n) for n=1..10000

Crossrefs

Cf. A000203, A065764, A072379 (partial sums).

Programs

Mathematica

Table[DivisorSigma[1, n]^2, {n, 1, 50}] (* Vaclav Kotesovec, Feb 05 2019 *)

PARI

a(n)=sigma(n)^2;  /* Joerg Arndt, Oct 07 2012 */

Formula

Dirichlet g.f.: zeta(s)*zeta(s-1)^2*zeta(s-2)/zeta(2*s-2), Re(s)>3. - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jul 21 2002

From Vladeta Jovovic, Jul 30 2002: (Start)

Multiplicative with a(p^e) = ((p^(e+1)-1)/(p-1))^2.

a(n) = Sum_{d|n} n/d*sigma(d^2). (End)

Equals the Dirichlet convolution of A065764 by A000027: a(n) = sigma(n^2) * n. - R. J. Mathar, Apr 02 2011

Sum_{k>=1} 1/a(k) = A109693 = 1.3064565120389505680107494870912715497583907915664910373609699598615342645... - Vaclav Kotesovec, Sep 20 2020