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A064944 a(n) = Sum_{i|n, j|n, j >= i} j.

%I A064944 #35 Aug 09 2025 10:07:54
%S A064944 1,5,7,17,11,38,15,49,34,60,23,132,27,82,82,129,35,191,39,207,112,126,
%T A064944 47,384,86,148,142,283,59,469,63,321,172,192,172,666,75,214,202,597,
%U A064944 83,640,87,435,403,258,95,1016,162,485,262,511,107,812,264,813,292,324
%N A064944 a(n) = Sum_{i|n, j|n, j >= i} j.
%H A064944 Paolo Xausa, <a href="/A064944/b064944.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)
%F A064944 a(n) = Sum_{i=1..tau(n)} i*d_i, where {d_i}, i=1..tau(n) is the increasing sequence of divisors of n.
%F A064944 a(n) = Sum_{i=1..A000005(n)} i*A027750(n, i). - _Michel Marcus_, Jun 10 2015
%F A064944 From _Ridouane Oudra_, Aug 01 2025: (Start)
%F A064944 a(n) = Sum_{d|n} (n/d)*A135539(n,d).
%F A064944 a(n) = A064946(n) + A000203(n).
%F A064944 a(n) = (A064948(n) + A000203(n))/2.
%F A064944 a(n) = A337360(n) - A064945(n).
%F A064944 a(n) = A064948(n) - A064946(n).
%F A064944 a(n) = A064840(n) - A064947(n). (End)
%e A064944 a(6) = max(1,1)+max(1,2)+max(1,3)+max(1,6)+max(2,2)+max(2,3)+max(2,6)+max(3,3)+max(3,6)+max(6,6)=38, or a(6) = dot_product(1,2,3,4)*(1,2,3,6)=1*1+2*2+3*3+4*6=38.
%p A064944 with(numtheory): seq(add(i*sort(convert(divisors(n),'list'))[i],i=1..tau(n)), n=1..200);
%t A064944 A064944[n_] := #.Range[Length[#]] & [Divisors[n]];
%t A064944 Array[A064944, 100] (* _Paolo Xausa_, Aug 07 2025 *)
%o A064944 (PARI) a(n) = my(d=divisors(n)); sum(i=1, length(d), i*d[i]); \\ _Harry J. Smith_, Sep 30 2009
%o A064944 (Haskell)
%o A064944 a064944 = sum . zipWith (*) [1..] . a027750_row'
%o A064944 -- _Reinhard Zumkeller_, Jul 14 2015
%o A064944 (Python)
%o A064944 from sympy import divisors
%o A064944 def A064944(n): return sum(a*b for a, b in enumerate(divisors(n),1)) # _Chai Wah Wu_, Aug 07 2025
%Y A064944 Cf. A060640, A064945, A064946, A064947, A064948, A064949.
%Y A064944 Cf. A027750, A135539, A000005, A000203, A064840, A337360, A337297.
%K A064944 nonn
%O A064944 1,2
%A A064944 _Vladeta Jovovic_, Oct 28 2001