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A064949 a(n) = Sum_{i|n, j|n} min(i,j).

%I A064949 #30 Aug 18 2025 20:02:18
%S A064949 1,5,6,15,8,32,10,37,23,42,14,100,16,52,52,83,20,125,22,132,64,72,26,
%T A064949 252,45,82,76,162,32,286,34,177,88,102,88,397,40,112,100,336,44,352,
%U A064949 46,222,208,132,50,572,75,239,124,252,56,416,120,414,136,162,62,916,64
%N A064949 a(n) = Sum_{i|n, j|n} min(i,j).
%H A064949 Antti Karttunen, <a href="/A064949/b064949.txt">Table of n, a(n) for n = 1..20000</a> (first 1000 terms from Harry J. Smith)
%F A064949 a(n) = Sum_{i=1..tau(n)} (2*tau(n)-2*i+1)*d_i, where {d_i}, i=1..tau(n), is increasing sequence of divisors of n.
%F A064949 a(n) = Sum_{i=1..n} A135539(n,i)^2. - _Ridouane Oudra_, Oct 25 2021
%F A064949 a(n) = A000203(n) * (2*A000005(n)+1) - 2*A064944(n). - _Amiram Eldar_, Jan 13 2025
%F A064949 From _Ridouane Oudra_, Aug 13 2025: (Start)
%F A064949 a(n) = A064945(n) + A064947(n).
%F A064949 a(n) = 2*A064947(n) + A000203(n).
%F A064949 a(n) = 2*A064945(n) - A000203(n).
%F A064949 a(n) = 2*A064840(n) - A064948(n). (End)
%e A064949 a(6) = dot_product(7,5,3,1)*(1,2,3,6) = 7*1 + 5*2 + 3*3 + 1*6 = 32.
%p A064949 with(numtheory): seq(add((2*tau(n)-2*i+1)*sort(convert(divisors(n),'list'))[i],i=1..tau(n)), n=1..200);
%t A064949 Array[Function[{t, d}, Total@ MapIndexed[#1 (2 t - 2 First[#2] + 1) &, d]] @@ {DivisorSigma[0, #], Divisors[#]} &, 61] (* _Michael De Vlieger_, Oct 25 2021 *)
%o A064949 (PARI) a(n) = { my(d=divisors(n), t=length(d)); sum(i=1, t, (2*t - 2*i + 1)*d[i]) } \\ _Harry J. Smith_, Oct 01 2009
%o A064949 (PARI) A064949(n) = { my(i=0, u=numdiv(n)); sumdiv(n,d,i++; (((2*u)-(2*i))+1)*d); }; \\ _Antti Karttunen_, Nov 14 2021
%Y A064949 Cf. A000005, A000203, A064944, A064945, A135539, A064840.
%K A064949 nonn
%O A064949 1,2
%A A064949 _Vladeta Jovovic_, Oct 28 2001