%I #17 Dec 11 2023 10:50:15

%S 1,9,13,45,21,117,29,173,94,189,45,585,53,261,273,573,69,846,77,945,

%T 377,405,93,2249,246,477,526,1305,117,2457,125,1725,585,621,609,4230,

%U 149,693,689,3633,165,3393,173,2025,1974,837,189,7449,470,2214,897

%N a(n) = Sum_{d|n} d*tau(d)^2.

%H Amiram Eldar, <a href="/A068984/b068984.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = (p^(e+3)-3*p^(e+2)+4*p^(e+1)-p-1+2*p^(e+3)*e-6*p^(e+2)*e+4*p^(e+1)*e+p^(e+3)*e^2-2*p^(e+2)*e^2+p^(e+1)*e^2)/(p-1)^3.

%t a[n_] := DivisorSum[n, # * DivisorSigma[0, #]^2 &]; Array[a, 100] (* _Amiram Eldar_, Sep 15 2019 *)

%o (PARI) a(n) = sumdiv(n, d, d*numdiv(d)^2) \\ _Michel Marcus_, Jun 17 2013

%o (Magma) [&+[d*#Divisors(d)^2: d in Divisors(n)]:n in [1..51]]; // _Marius A. Burtea_, Sep 15 2019

%Y Cf. A000005, A062369, A060724, A064950.

%K mult,nonn

%O 1,2

%A _Vladeta Jovovic_, Apr 01 2002