cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A072861 #24 Nov 08 2023 00:01:53
%S A072861 1,9,16,49,36,144,64,225,169,324,144,784,196,576,576,961,324,1521,400,
%T A072861 1764,1024,1296,576,3600,961,1764,1600,3136,900,5184,1024,3969,2304,
%U A072861 2916,2304,8281,1444,3600,3136,8100,1764,9216,1936,7056,6084,5184,2304,15376,3249
%N A072861 a(n) = sigma(n)^2.
%D A072861 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)
%H A072861 J. G. Wurtzel, <a href="/A072861/b072861.txt">Table of n, a(n) for n=1..10000</a>
%F A072861 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
%F A072861 From _Vladeta Jovovic_, Jul 30 2002: (Start)
%F A072861 Multiplicative with a(p^e) = ((p^(e+1)-1)/(p-1))^2.
%F A072861 a(n) = Sum_{d|n} n/d*sigma(d^2). (End)
%F A072861 Equals the Dirichlet convolution of A065764 by A000027: a(n) = sigma(n^2) * n. - _R. J. Mathar_, Apr 02 2011
%F A072861 Sum_{k>=1} 1/a(k) = A109693 = 1.3064565120389505680107494870912715497583907915664910373609699598615342645... - _Vaclav Kotesovec_, Sep 20 2020
%t A072861 Table[DivisorSigma[1, n]^2, {n, 1, 50}] (* _Vaclav Kotesovec_, Feb 05 2019 *)
%o A072861 (PARI) a(n)=sigma(n)^2;  /* _Joerg Arndt_, Oct 07 2012 */
%Y A072861 Cf. A000203, A065764, A072379 (partial sums).
%K A072861 nonn,mult
%O A072861 1,2
%A A072861 _N. J. A. Sloane_, Jul 26 2002