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A064947 a(n) = Sum_{i|n, j|n, j>i} i.

%I A064947 #32 Aug 13 2025 21:32:17
%S A064947 0,1,1,4,1,10,1,11,5,12,1,36,1,14,14,26,1,43,1,45,16,18,1,96,7,20,18,
%T A064947 53,1,107,1,57,20,24,20,153,1,26,22,123,1,128,1,69,65,30,1,224,9,73,
%U A064947 26,77,1,148,24,147,28,36,1,374,1,38,77,120,26,168,1,93,32,165,1,411,1,44
%N A064947 a(n) = Sum_{i|n, j|n, j>i} i.
%C A064947 For given n, iterate a(n); a(a(n)); a(a(a(n))); ... Does this iterative process always lead to a(a(...(a(n))...)) = 1? - _Ctibor O. Zizka_, Apr 17 2008
%C A064947 No. For example, a(4) = 4, a(14) = 14, and a(99) = 99. - _Jason Yuen_, Jan 07 2025
%H A064947 Harry J. Smith, <a href="/A064947/b064947.txt">Table of n, a(n) for n = 1..1000</a>
%F A064947 a(n) = Sum_{i=1..tau(n)} (tau(n)-i)*d_i, where {d_i}, i=1..tau(n), is increasing sequence of divisors of n.
%F A064947 From _Ridouane Oudra_, Aug 07 2025: (Start)
%F A064947 a(n) = A064945(n) - A000203(n).
%F A064947 a(n) = A064840(n) - A064944(n).
%F A064947 a(n) = A064949(n) - A064945(n).
%F A064947 a(n) = A337297(n) - A064946(n).
%F A064947 a(n) = (A064949(n) - A000203(n))/2. (End)
%e A064947 a(6) = dot_product(3,2,1,0)*(1,2,3,6) = 3*1 + 2*2 + 1*3 + 0*6 = 10.
%p A064947 with(numtheory): seq(add((tau(n)-i)*sort(convert(divisors(n),'list'))[i],i=1..tau(n)), n=1..200);
%t A064947 Table[t = DivisorSigma[0, n]; Total@ MapIndexed[(t - First[#2])*#1 &, Divisors[n]], {n, 120}] (* _Michael De Vlieger_, Jan 07 2025 *)
%o A064947 (PARI) a(n) = my(d=divisors(n), t=length(d)); sum(i=1, t - 1, (t - i)*d[i]); \\ _Harry J. Smith_, Oct 01 2009
%Y A064947 Cf. A000005, A000203, A064840, A337297, A027750.
%K A064947 nonn
%O A064947 1,4
%A A064947 _Vladeta Jovovic_, Oct 28 2001