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A064948 a(n) = Sum_{i|n, j|n} max(i,j).

%I A064948 #22 Aug 14 2025 03:58:47
%S A064948 1,7,10,27,16,64,22,83,55,102,34,236,40,140,140,227,52,343,58,372,192,
%T A064948 216,70,708,141,254,244,510,88,866,94,579,296,330,296,1241,112,368,
%U A064948 348,1104,124,1184,130,786,728,444,142,1908,267,877,452,924,160,1504,456
%N A064948 a(n) = Sum_{i|n, j|n} max(i,j).
%H A064948 Harry J. Smith, <a href="/A064948/b064948.txt">Table of n, a(n) for n = 1..1000</a>
%F A064948 a(n) = Sum_{i=1..tau(n)} (2*i-1)*d_i, where {d_i}, i=1..tau(n), is the increasing sequence of the divisors of n.
%F A064948 a(n) = 2*A064944(n) - A000203(n). - _Amiram Eldar_, Dec 23 2024
%F A064948 From _Ridouane Oudra_, Aug 07 2025: (Start)
%F A064948 a(n) = A064944(n) + A064946(n).
%F A064948 a(n) = 2*A064946(n) + A000203(n).
%F A064948 a(n) = 2*A064840(n) - A064949(n). (End)
%e A064948 a(6) = dot_product(1,3,5,7)*(1,2,3,6) = 1*1 + 3*2 + 5*3 + 7*6 = 64.
%p A064948 with(numtheory): seq(add((2*i-1)*sort(convert(divisors(n),'list'))[i],i=1..tau(n)), n=1..200);
%t A064948 A064948[n_] := #.(2*Range[Length[#]] - 1) & [Divisors[n]];
%t A064948 Array[A064948, 100] (* _Paolo Xausa_, Aug 14 2025 *)
%o A064948 (PARI) a(n) = { my(d=divisors(n)); sum(i=1, #d, (2*i - 1)*d[i]) } \\ _Harry J. Smith_, Oct 01 2009
%Y A064948 Cf. A000005, A000203, A064944, A064840.
%K A064948 nonn
%O A064948 1,2
%A A064948 _Vladeta Jovovic_, Oct 28 2001