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.
%I A064945 #52 Aug 09 2025 10:09:25
%S A064945 1,4,5,11,7,22,9,26,18,30,13,64,15,38,38,57,19,82,21,87,48,54,25,156,
%T A064945 38,62,58,109,31,179,33,120,68,78,68,244,39,86,78,213,43,224,45,153,
%U A064945 143,102,49,348,66,166,98,175,55,268,96,267,108,126,61,542,63,134,181
%N A064945 a(n) = Sum_{i|n, j|n, j >= i} i.
%H A064945 Paolo Xausa, <a href="/A064945/b064945.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)
%F A064945 a(n) = Sum_{i=1..tau(n)} (tau(n)-i+1)*d_i, where {d_i}, i=1..tau(n), is the increasing sequence of divisors of n.
%F A064945 a(n) = Sum_{i=1..A000005(n)} (A000005(n)-i+1)*A027750(n, i). - _Michel Marcus_, Jun 10 2015
%F A064945 From _Ridouane Oudra_, Aug 02 2025: (Start)
%F A064945 a(n) = Sum_{d|n} d*A135539(n,d).
%F A064945 a(n) = A064947(n) + A000203(n).
%F A064945 a(n) = (A064949(n) + A000203(n))/2.
%F A064945 a(n) = A064949(n) - A064947(n).
%F A064945 a(n) = A337360(n) - A064944(n).
%F A064945 a(n) = A064840(n) - A064946(n). (End)
%e A064945 a(6) = dot_product(4,3,2,1)*(1,2,3,6) = 4*1+3*2+2*3+1*6 = 22.
%p A064945 with(numtheory): seq(add((tau(n)-i+1)*sort(convert(divisors(n),'list'))[i],i=1..tau(n)), n=1..200);
%t A064945 A064945[n_] := #.Range[Length[#], 1, -1] & [Divisors[n]];
%t A064945 Array[A064945, 100] (* _Paolo Xausa_, Aug 07 2025 *)
%o A064945 (PARI) a(n) = my(d=divisors(n), t=length(d)); sum(i=1, t, (t - i + 1)*d[i]); \\ _Harry J. Smith_, Oct 01 2009
%o A064945 (PARI) a(n)=my(d=divisors(n)); sum(i=1,#d,(#d+1-i)*d[i]) \\ _Charles R Greathouse IV_, Jun 10 2015
%o A064945 (Haskell)
%o A064945 a064945 = sum . zipWith (*) [1..] . reverse . a027750_row'
%o A064945 -- _Reinhard Zumkeller_, Jul 14 2015
%o A064945 (Python)
%o A064945 from sympy import divisors, divisor_sigma
%o A064945 def A064945(n): return (divisor_sigma(n,0)+1)*divisor_sigma(n)-sum(a*b for a, b in enumerate(divisors(n),1)) # _Chai Wah Wu_, Aug 07 2025
%Y A064945 Cf. A060640, A064944, A064946, A064947, A064948, A064949.
%Y A064945 Cf. A027750, A135539, A000005, A000203, A064840, A337360, A337297.
%Y A064945 Cf. A386911.
%K A064945 nonn,easy
%O A064945 1,2
%A A064945 _Vladeta Jovovic_, Oct 28 2001